Find f (1). 2. (1 pt) set1/p1-7.pg Find the equation of the line tangent to the curve. y = 2x 2 8x + 8 at the point

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1 Math 20-90, Fall 2008 WeBWorK Assignment due 09/03/2008 at 0:59pm MDT Polynomial calculus: Straight lines ; The slope of a curve; The derivative of a polynomial This assignment will cover the material from the Polynomial Calculus Notes sections 3a.. ( pt) set/p-6.pg Find the derivative of f(x)=3x 7. f (x) = 2. ( pt) set/p-7.pg Find the equation of the line tangent to the curve 5. ( pt) set/p-0.pg For what values of x does the curve y = x 2 2x + 3 have: Positive slope? Negative slope? Zero slope? x= Your answer to parts and 2 should be an interval (a,b). Use INF for +, -INF for. 6. ( pt) set/p-2.pg If f (x) = 5x 2 9x 4, find f (x). Find f (). y = 2x 2 8x + 8 at the point (4,8). (A line is tangent to a curve at a point if it passes through that point and the line and the curve have the same slope at that point. Although it is more natural to use the point-slope form, this question asks for the slope-intercept form.) y = 3. ( pt) set/p-8.pg Find the derivative of f(x)=x 9 6x 7 + 2x. f (x) = 4. ( pt) set/p-9.pg Find the slope of the curve y = 6x 5 9x 4 at the point (, 3). m = 7. ( pt) set/p-3.pg If f (x) = (2x 2 7)(5x + 5), find f (x). [NOTE: Your answer should be a function in terms of the variable x and not a number! ] 8. ( pt) set/p-4.pg Find the slope of the curve y = 3x 3 4x 2 + 3x + 3 at the point where x =. Slope at x = :.

2 Math 20-90, Fall 2008 WeBWorK Assignment 2 due 09/0/2008 at 0:59pm MDT Polynomial Calculus: Velocity and acceleration; The antiderivative of a polynomial; Definite integrals; The fundamental theorem (polynomials); General power rule derivatives and anti-derivatives. This assignment will cover the material from the Polynomial Calculus Notes sections 3b 5b as well as Theorem A on page 33 of the text which states that the power rule holds for rational (including negative integer) powers. (In fact, the rule holds for all real powers.). ( pt) set2/p-.pg a. Find the slope of the line passing through the points (0,5) and (7,9). b. Find the slope of the line passing through the points (2,3) and (3,5). 2. ( pt) set2/p-2.pg Find the equation of the line passing through the point (2,0) with slope 9. y= 3. ( pt) set2/p-3.pg The equation of the line passing through the point ( 9, 6) which is perpendicular to the line given by the equation 4x + 2y = is y = Ax + B where A= B= 4. ( pt) set2/p-4.pg Find the equation of the line passing through the point (-5,-0) and parallel to the line passing through (-0,-) and (0,0). y= 5. ( pt) set2/p-5.pg Find the equation of the line which bisects the line segment from (0,0) to (0,2) at right angles. y= 6. ( pt) set2/p2-2.pg If f (x) = x + 6 x 2, find f (x). Find f (). 7. ( pt) set2/p2-3.pg Find the x coordinate of the point on the curve y = x+5x,x > 0 where the tangent line has slope -. x= 8. ( pt) set2/p2-4.pg If f (t) = 5 t 4, find f (t). [NOTE: Your answer should be a function in terms of the variable t and not a number! ] 9. ( pt) set2/p3-3.pg Find the values of x at which the curve given by the equation 3 x3.5x 2 + 2x + 6 has a horizontal tangent line. Write your answers in increasing order. x =, 0. ( pt) set2/p4-0.pg Find the x coordinate of the point on the curve y = 0x 2 + 4x + 0 where the tangent line is perpendicular to the line x+5y =. (A line is tangent to a curve at a point if the line and the curve have the same slope at that point, and the line passes through that point.) x=. ( pt) set2/p-.pg Consider the function f (x) = 6x 3 7x 2 + 8x 0. An antiderivative of f (x) is F(x) = Ax 4 + Bx 3 +Cx 2 + Dx where A is and B is and C is and D is 2. ( pt) set2/p-2.pg Consider the function f (x) = 2x 0 + 9x 6 4x 3 9. Enter an antiderivative of f (x) 3. ( pt) set2/p-3.pg Consider the function f (x) = 3 x 2 6 x 5. Let F(x) be the antiderivative of f (x) with F() = 0. Then F(x) = 4. ( pt) set2/p-7.pg A car traveling at 50 ft/sec decelerates at a constant 6 ft/sec/sec. How many feet does the car travel before coming to a complete stop? 5. ( pt) set2/p-.pg A ball is thrown straight up so its height t seconds later is 6t t + 6. a. Find the velocity of the ball at t seconds after it is thrown. b. At what time does the ball reach its maximum height? t= c. Find the acceleration of the ball at any time t. a=

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4 Math 20-90, Fall 2008 WeBWorK Assignment 5 due 09/24/2008 at 0:59pm MDT Introduction to Limits; Rigorous Study of Limits; Limit Theorems. This assignment will cover the material from Sections..3.. ( pt) set5/s 3 9.pg Evaluate the limit 2. ( pt) set5/s 3 22.pg Evaluate the limit s 3 s lim s s 2 s 3 lim s s 2 7. ( pt) set5/ns2 2 xx.pg Let f (x) = 6 if x > 6, f (x) = 7 if x = 6, f (x) = x + if 2 x < 6, f (x) = 3 if x < 2. Sketch the graph of this function and find following limits if they exist (if not, enter DNE).. lim x 6 2. lim x lim f (x) x 6 4. lim x 2 5. lim x lim x 2 3. ( pt) set5/s 3 27.pg Evaluate the limit lim b b 7 b 8. ( pt) set5/p3-0.pg Evaluate the limit 3(3 + h) 2 + 2(3 + h) ( ) lim h 0 h 4. ( pt) set5/s 3 36.pg Evaluate the limit 5. ( pt) set5/s 3 48.pg Evaluate the limit 6. ( pt) set5/ns2 2 x.pg Let f (x) = x + if x 4 and f (x) = if x > 4. lim x x x s + 6 lim s 6 s + 6 Sketch the graph of this function for yourself and find following limits if they exist (if not, enter N).. lim x 4 f (x) 2. lim x 4 + f (x) 3. lim x 4 f (x) 9. ( pt) set5/gross 20 summer2000 set3 prob5.pg If an arrow is shot straight upward on the moon with a velocity of 56 m/s, its height (in meters) after t seconds is given by h = 56t 0.83t 2. What is the velocity of the arrow (in m/s) after 9 seconds? After how many seconds will the arrow hit the moon? With what velocity (in m/s) will the arrow hit the moon? 0. ( pt) set5/gross 20 summer2000 set3 prob3.pg Find the slope of the tangent line to the parabola y = 3x 2 +3x+2 at x 0 = 0. (The tangent line to a curve at a point is the line passing through that point whose slope is the same as the slope of the curve at that point.) The equation of this tangent line can be written in the form y y 0 = m(x x 0 ) where y 0 is:

5 Math 20-90, Fall 2008 WeBWorK Assignment 6 due 0/0/2008 at 0:59pm MDT Limits Involving Trigonometric Functions; Limits at Infinity, Infinite Limits; Continuity of Functions This assignment will cover the material from Sections ( pt) set6/p2-9.pg Evaluate the limit 2. ( pt) set6/p2-0.pg Evaluate the limit sin8x lim x 0 sin3x tanx lim x 0 3x 3. ( pt) set6/s 5 38.pg For what value of the constant c is the function f continuous on (, ) where { s 2 c if s (,9) f (s) = cs + 4 if s [9, ) 4. ( pt) set6/cs5p5.pg The function f is given by the formula f (x) = 2x3 4x 2 25x 25 x + 5 when x < 5 and by the formula f (x) = 5x 2 + x + a when 5 x. What value must be chosen for a in order to make this function continuous at -5? a = 5. ( pt) set6/ur lr 3 8.pg Evaluate the following limits. If needed, enter INF for + and MINF for. (a) 0x + 6 lim x + 5x 2 9x + 6 (b) lim x 6. ( pt) set6/ur lr 3.pg 0x + 6 5x 2 9x + 6 Evaluate the following limits. If needed, enter INF for + and MINF for. (a) (b) lim x + lim x 7. ( pt) set6/ur lr 3 3.pg 5 + 2x x = 5 + 2x x = Evaluate the following limits. If needed, enter INF for + and MINF for. (a) ( ) lim x 2 4x + x = x + (b) 8. ( pt) set6/ur lr 3 5.pg ( ) lim x 2 4x + x = x Evaluate the following limits. If needed, enter INF for and MINF for. (a) (b) lim x x 5 8x = 2x lim x 5 5 8x = 8

6 Math 20-90, Fall 2008 WeBWorK Assignment 7 due 0/08/2008 at 0:59pm MDT Two Problems and One Theme; The Derivative; Rules for Finding Derivatives. This assignment will cover the material from Sections If. ( pt) set7/p2-.pg find f (x). Find f (4). 2. ( pt) set7/p2-5.pg If f (x) = 5x+7 6x+5, find f (x). f (x) = x 7 x + 7 Find f (). 3. ( pt) set7/p3-4.pg A traveler is moving from left to right along the curve y = x 2. When she shuts off the engines, she will continue traveling along the tangent line at the point where she is at that time. At what point should she cut off the engines in order to reach the point (3,5)? x= 4. ( pt) set7/p3-6.pg Let f (x) = x2 +9 x+9. Then f (x) = 5. ( pt) set7/p3-0.pg Find the equation of the tangent line to the curve y = (x + )(x 2 ) at the point (,0). y =

7 Math 20-90, Fall 2008 WeBWorK Assignment 8 due 0/22/2008 at 0:59pm MDT Derivatives of Trigonometric Functions; The Chain Rule; Higher-Order Derivatives. This assignment will cover the material from Sections ( pt) set8/p2-6.pg Let f (x) = 2x +2x. Then f (3) is and f (3) is and f (3) is 6. ( pt) set8/p2-3.pg If find f (x). Find f (). f (x) = tanx 4 secx 2. ( pt) set8/p2-7.pg The angle of elevation to the top of a building is found to be 9 from the ground at a distance of 6000 feet from the base of the building. Find the height of the building. Hint: Did you convert degrees to radians? (Show hint after 5 attempts. ) 7. ( pt) set8/p2-4.pg Let f ( π 2 ) = 8. ( pt) set8/p2-5.pg If f (x) = sin(x 2 ), find f (x). f (x) = 2xsinxcosx 3. ( pt) set8/p2-8.pg A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 25. From a point 500 feet closer to the mountain along the plain, they find that the angle of elevation is 29. How high (in feet) is the mountain? Hint: Did you convert degrees to radians? (Show hint after 5 attempts. ) If 4. ( pt) set8/p2-.pg find f (x). Find f (3). 5. ( pt) set8/p2-2.pg If f (x) = 2tanx x, find f (x). Find f (5). f (x) = 2sinx + cosx Find f (5). 9. ( pt) set8/p2-6.pg Let f (x) = 0cos(x)+0sin(x) cos(x). Find f (x). f (x) = 0. ( pt) set8/p3-.pg A point is rotating about the circle of radius in the counterclockwise direction. It takes 4.2 minutes to make one revolution. Assuming it starts on the positive x-axis, what are the coordinates of the point in.4 minutes? x = y =. ( pt) set8/p4-.pg Let f (x) = (cos(3x) + 8) 7. Find f (x). f (x) = 2. ( pt) set8/p4-2.pg Let y = (3sin(2x) + 2) 3. What is the slope of the tangent line to the curve when x = π 6? 3. ( pt) set8/p4-3.pg Let f (x) = ( x 2 4 ) 2. For what values of x is f (x) = 0? Write the answers in increasing order.,.

8 4. ( pt) set8/p4-4.pg Let f (x) = 3x 2 + 5x + 3 f (x) = f (2) = 5. ( pt) set8/p4-5.pg If f (x) = sin(x 4 ), find f (x). Find f (3). f (x) = 7. ( pt) set8/p4-7.pg Let f (x) = 8. ( pt) set8/p4-9.pg Let f (x) = x /3 (2x + 4) /2. f (x) = f (8) = f (x) = sin(4x 2) 6. ( pt) set8/p4-6.pg Let f (x) = 3sin 3 x 9. ( pt) set8/p3-5.pg Let f (x) = x x 5. Then f (x) = f (x) = 20. ( pt) set8/p3-7.pg Let f (x) = (x + 2) ( x 2 9 ). For what value of x is f (x) = 0? 2

9 Math 20-90, Fall 2008 WeBWorK Assignment 9 due 0/29/2008 at 0:59pm MDT Implicit Differentiation; Related Rates; Differentials and Approximations. This assignment will cover the material from Sections ( pt) set9/p3-.pg Let y = 4x 2. Find the change in y, y when x = and x = 0.2 Find the differential dy when x = and dx = ( pt) set9/p3-2.pg Use linear approximation, i.e. the tangent line, to approximate as follows: Let f (x) = 3 x. The equation of the tangent line to f (x) at x = 25 can be written in the form y = mx + b where m is: and where b is: Using this, we find our approximation for is 3. ( pt) set9/p5-.pg Find the slope of the tangent line to the curve at the point ( 8,2). x 2 xy + 2y 3 = ( pt) set9/p5-2.pg Use implicit differentiation to find the slope of the tangent line to the curve y x 5y = x4 + 7 at the point (, 8 4 ). m = 5. ( pt) set9/p5-3.pg Find the coordinates of those points on the curve given by the equation x 2.25xy + y 2 = 6 at which the tangent line has slope. The first point must be the one with the greater x coordinate.,, 6. ( pt) set9/p5-4.pg Find the x coordinate of the point on the curve x 2 + 0xy = 6 where the tangent line is parallel to the line 8x + y = 9. There are two answers; submit the greater answer first. x =, 7. ( pt) set9/p5-5.pg If the variables s and t are related by the equation find ds dt implicitly. ds dt = st + 8t 3 = 9 8. ( pt) set9/p5-6.pg If f is the focal length of a convex lens and an object is placed at a distance q from the lens, then its image will be at a distance p from the lens, where f, q, and p are related by the lens equation f = q + p Suppose the focal length of a particular lens is 20 cm. What is the rate of change of q with respect to p when p = 7? (Make sure you have the correct sign for the rate.) dq d p = 9. ( pt) set9/p5-7.pg A street light is at the top of a ft. tall pole. A man ft tall walks away from the pole with a speed of feet/sec along a straight path. How fast is the tip of his shadow moving away from the pole when the man is feet from the pole? ft/sec 0. ( pt) set9/p5-8.pg A spherical snowball is melting in such a way that its radius is decreasing at the rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 4.5 cm? (Note the answer is a positive number). cm 3 /min. ( pt) set9/p5-9.pg Sand falls out of the end of a slurry at the rate of 40 cc/sec. The pile forms a circular cone, the ratio of whose base diameter to height is 3. When the pile is of height 20 cm., at what rate is the height of the pile increasing? dh dt = 2. ( pt) set9/p5-0.pg Water is flowing into a balloon at the rate of 20 cc/min. The balloon has a puncture, and the rate at which water flows out of the balloon at this puncture is proportional to the volume of water in the balloon. Let the proportionality constant be At what volume do we have equilibrium (that is the volume of water in the balloon remains constant)? Hint: if we let W i represent the amount of water which flows in, and W o the amount flowing out of the puncture, we have dw i dt = 20 and dw o dt = 0.28V where V is the volume of water in the balloon. V = 3. ( pt) set9/p4-8.pg Given that d dx ( f (3x 5 )) = 8x 4, find a formula for the derivative of f. Hint: let u = 3x 5, and write down the chain rule: df/dx = (df/du)(du/dx), and solve for df/du. The answer is in terms of x; rewrite it in terms of u. f (u) =

10 4. ( pt) set9/p6-.pg If the variables x and y are related by the equation find dy dx and d2 y dx 2 implicitly. x 3 + y 3 = 2 (a) dy dx = (b) d2 y = dx 2 (For part (b), differentiate part (a) implicitly, substitute for dy/dx using part (a), and simplify using the original equation.) 2

11 Math 20-90, Fall 2008 WeBWorK Assignment 0 due /05/2008 at 0:59pm MST Maxima and Minima; Monotonicity and Concavity; Local Extrema and Extrema on Open Intervals; Practical Problems; Graphing Functions Using Calculus. This assignment will cover the material from Sections ( pt) set0/p6-.pg Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false. A good technique is to think of several examples, especially examples which might show that the statement is false! You must get all of the answers correct to receive credit.. If the linear approximation of a differentiable function is constant at a point a then the function could be decreasing near the point a. 2. Every continuous function whose domain is a bounded, closed interval has a maximum value. 3. Every differentiable function is continuous. 4. If f (x) is a continuous function and the sequence a,a 2,a 3,... converges to a finite limit, then the sequence f (a ), f (a 2 ), f (a 3 ),... also converges to a limit. 5. Every differentiable function whose domain is a bounded, closed interval and which has a maximum value also has a minimum value. 6. If a function is increasing near a point a then its linear approximation at a cannot be decreasing. 7. If a differentiable function has a maximum value then its domain must be a bounded, closed interval. 8. If a continuous function has a maximum value then its domain must be a bounded, closed interval. over the closed interval [a,b] where a = and b =. 5. ( pt) set0/p6-6.pg The function f (x) = 2x 3 3x 2 2x 4 is decreasing on the interval (, ). It is increasing on the interval (, ) and the interval (, ). The function has a local maximum at. 6. ( pt) set0/p6-7.pg For x [ 4,] the function f is defined by f (x) = x 6 (x 4) 3 On which two intervals is the function increasing? to and to Find the region in which the function is positive: Where does the function achieve its minimum? 7. ( pt) set0/p6-8.pg Identify the interior critical points and find the maximum value and minimum value of the following function on the given interval. f (x) = x 3 3x +, over [ 3/2,3]. Critical Points:,. Maximum:. Minimum:. to 2. ( pt) set0/p6-2.pg What number exceeds its square by the maximum amount? Begin by convincing yourself that this number is on the interval [0,]. Answer:. 3. ( pt) set0/p6-3.pg Consider the function f (x) = 4 5x 2, 5 x 2. The absolute maximum value is and this occurs at x equals The absolute minimum value is and this occurs at x equals 4. ( pt) set0/p6-5.pg Let Q = (0,7) and R = (9,0) be given points in the plane. We want to find the point P = (x,0) on the x-axis such that the sum of distances PQ + PR is as small as possible. (Before proceeding with this problem, draw a picture!) To solve this problem, we need to minimize the following function of x: f (x) = Instructions: ) When entering the critical points, please enter them in the order that they appear on the real line. 2) If the function has no critical points, enter the string NONE in all answer boxes for critical points. Some treatments of Calculus such as Varberg, Purcell, and Rigdon include the endpoints of a closed interval among its critical points, while others do not, and would not require us exclude them with the word interior. 8. ( pt) set0/p6-9.pg Consider the function f (x) = 8(x 5) 2/3. For this function there are two important intervals: (,A) and (A, ) where A is a critical number. Find A For each of the following intervals, tell whether f (x) is increasing (type in INC) or decreasing (type in DEC). (,A): (A, ):

12 9. ( pt) set0/p6-0.pg Find the length of the shortest line from the origin to the line y = 8x. d = Find the dimensions of the rectangle of greatest area. Answer: x = y = 0. ( pt) set0/p7-.pg A racer can cycle around a circular loop at the rate of 4 revolutions per hour. Another cyclist can cycle the same loop at the rate of 9 revolutions per hour. If they start at the same time (t=0), at what first time are they farthest apart? t = hours.. ( pt) set0/p7-2.pg Two men are at opposite corners of a square block which is 500 feet on a side. They start to walk at the same time; one man walking east at the rate of 2 feet per second, and the other walks west at the rate of 2 feet per second. At what time are they closest? t = seconds. 2. ( pt) set0/p7-3.pg A rectangle is to be drawn in the first quadrant with one leg on the y-axis, and the other on the x-axis, and a vertex on the curve y = 0.39x 2. Find the coordinates of that vertex which form the rectangle of greatest area. x = y = 3. ( pt) set0/p7-4.pg The illumination at a point is inversely proportional to the square of the distance of the point from the light source and directly proportional to the intensity of the light source. If two light sources are 40 feet apart and their intensities are 80 and 70 respectively, at what point between them will the sum of their illuminations be a minimum? Solution: Let x be the distance from the brighter source at which the sum of the illuminations is a minimum. Then x = feet. 4. ( pt) set0/p7-5.pg A rectangle with sides parallel to to the coordinate axes is inscribed in the ellipse 6x 2 + 6y 2 = ( pt) set0/p7-6.pg A drum in the form of a circular cylinder and open at one of the circular ends, is to be made so as to contain one cubic yard. Find the dimensions of the drum (height h and base radius r ) which minimizes the amount of material going into the drum. The surface area of the drum includes the area of the cylinder and the circles at bottom. r = h = 6. ( pt) set0/p7-7.pg The Miraculous Widget Company is informed by its market analyst, that if the price of widgets is $60-x, the company will sell 00+5x thousand widgets. At what price should the widget be set so the company maximizes income? x= price= 7. ( pt) set0/p7-8.pg Another company sells wrought iron umbrella trees. This company has fixed costs of $00,000/month. The cost in labor and material is $5 per umbrella sold per month. To sell x items, the price must be set at $50-0.2x, where x is in thousands of umbrellas sold per month. What price will maximize profit? price= 8. ( pt) set0/p8-.pg Consider the function f (x) = 6x + 4x. For this function there are four important intervals: (, A], [A, B),(B,C], and [C, ) where A, and C are the critical numbers and the function is not defined at B. Find A and B and C For each of the following intervals, tell whether f (x) is increasing (type in INC) or decreasing (type in DEC). (,A]: [A,B): (B,C]: [C, ) Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f (x) is concave up (type in CU) or concave down (type in CD). (,B): (B, ):

13 9. ( pt) set0/p8-2.pg Answer the following questions for the function f (x) = x x 2 + defined on the interval [ 7,7]. A. f (x) is concave down on the region to B. f (x) is concave up on the region to C. The inflection point for this function is at D. The minimum for this function occurs at E. The maximum for this function occurs at 20. ( pt) set0/p8-3.pg Answer the following questions for the function f (x) = x x 2 6x x 2 6x + 0 defined on the interval [ 4,0]. If you factor out the radical and then note the similarity to the preceding problem, it becomes easy. A. f (x) is concave down on the region to B. f (x) is concave up on the region to C. The inflection point for this function is at D. The minimum for this function occurs at E. The maximum for this function occurs at 2. ( pt) set0/p8-4.pg Consider the function f (x) = 2x x 4 60x 3 +. f (x) has inflection points at (reading from left to right) x = D, E, and F where D is and E is and F is For each of the following intervals, tell whether f (x) is concave up (type in CU) or concave down (type in CD). (,D]: [D,E]: [E,F]: [F, ): 23. ( pt) set0/p8-6.pg Consider the function f (x) = 2x x 2 20x + 8. For this function there are three important intervals: (,A], [A,B], and [B, ) where A and B are the critical numbers. Find A and B For each of the following intervals, tell whether f (x) is increasing (type in INC) or decreasing (type in DEC). (,A]: [A,B]: [B, ) f (x) has an inflection point at x = C where C is Finally for each of the following intervals, tell whether f (x) is concave up (type in CU) or concave down (type in CD). (,C]: [C, ) 24. ( pt) set0/p8-7.pg NOTE: If there is no correct answer, submit NO. Let y = x2 6x + 5. a. The graph has vertical asymptotes along the lines x=a for a=. b. The horizontal asymptote is y=. c. As x approaches a from the left, y approaches. d. As x approaches a from the right, y approaches. e. The graph has a local maximum at x=. f. The graph has a local minimum at x=. g. The graph is increasing in the intervals (, ) and (, ). 22. ( pt) set0/p8-5.pg Consider the function f (x) = 3x+2 2x+4. For this function there are two important intervals: (,A) and (A, ) where the function is not defined at A. Find A For each of the following intervals, tell whether f (x) is increasing (type in INC) or decreasing (type in DEC). (,A): (A, ) Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether f (x) is concave up (type in CU) or concave down (type in CD). (,A): (A, ) ( pt) set0/p8-8.pg NOTE: If there is no correct answer, submit NO. Let y = x + 5 (x 5) 2 a. The graph has a vertical asymptote x=a for a=. b. The horizontal asymptote is y=. c. As x approaches a from the left, y approaches. d. As x approaches a from the right, y approaches. e. The graph has a local maximum at x=.

14 f. The graph has a local minimum at x=. g. The graph is increasing in the intervals (, ) and (, ). 29. ( pt) set0/c0sp4/c0sp4.pg 26. ( pt) set0/p8-9.pg NOTE: If there is no correct answer, submit NO. Let y = 9x a. The horizontal asymptote is y=. b. The graph has a local minimum at x=. c. The minimum value of y is y=. d. The graph has a local maximum at x=. 27. ( pt) set0/p8-0.pg NOTE: If there is no correct answer, submit NO. Consider the function y = sinx 2 + cosx defined over the interval [ π/2,π/2]. a. The graph has a vertical asymptote at x =. b. y < 0 for x in the interval between and. c. y is increasing for x in the interval between and. 28. ( pt) set0/p6-4.pg A rancher wants to fence in an area of square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use? Note: the answer is to be the length of fence which is a minimum, not the length of a side which achieves that minimum. The graph shown is the graph of the SLOPE of the tangent line of the original function. (This slope is also called the derivative of f.) For each interval, enter all letters whose corresponding statements are true for that interval.. The interval from a to b 2. The interval from b to c 3. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The slope of the original function is positive on this interval B. The slope of the original function is negative on this interval. C. The slope of the original function is increasing on this interval. D. The slope of the original function is decreasing on this interval. E. The original function is increasing on this interval. F. The original function is decreasing on this interval. G. The shape of the original function is concave up on this interval. H. The shape of the original function is concave down on this interval. 4

15 Math 20-90, Fall 2007 WeBWorK Assignment due /2/2008 at 0:59pm MST The Mean Value Theorem for Derivatives; Solving Equations Numerically; Antiderivatives (Indefinite Integrals); Introduction to Differential Equations. This assignment will cover the material from Sections ( pt) set/c3s2p.pg Consider the function f (x) = 3x 3 + x 2 + 4x 3 Find the average slope of this function on the interval ( 3,2). By the Mean Value Theorem, we know there exists a c in the open interval ( 3,2) such that f (c) is equal to this mean slope. Find the two values of c in the interval which work, enter the smaller root first: 2. ( pt) set/s3 2 3.pg Consider the function f (x) = x on the interval [4,]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (4,) such that f (c) is equal to this mean slope. For this problem, there is only one c that works. Find it. 3. ( pt) set/p0-2.pg Use the fixed point algorithm to find the positive value of x which satisfies x = cos(x). Give the answer to four places of accuracy. Remember to calculate the trig functions in radian mode. (Hint: Push the cos button on your calculator repeatedly?) 4. ( pt) set/s2 0 3.pg Use Newton s method to find an approximate solution to the equation x 3 + x = 4 as follows. Let x = be the initial approximation. The second approximation x 2 is and the third approximation x 3 is 5. ( pt) set/s2 0.pg Use Newton s method to approximate a root of the equation 5sin(x) = x as follows. Let x = be the initial approximation. The second approximation x 2 is and the third approximation x 3 is 6. ( pt) set/p-4.pg Consider the function f (t) = 0sec 2 (t) 9t 2. Let F(t) be the antiderivative of f (t) with F(0) = 0. Then F(t) equals 7. ( pt) set/pr.pg Consider the function f (x) = x 2 x on the interval [ 4,7]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval ( 4,7) such that f (c) is equal to this mean slope. Find c. c = 8. ( pt) set/p-8.pg Consider the differential equation: du dt = u2 (t 3 t). a) Find the general solution to the above differential equation. (Instruction: Write the answer in a form such that its numerator is and its integration constant is C rename your constant if necessary.) Answer: u =. b) Find the particular solution of the above differential equation that satisfies the condition u = 4 at t = 0. Answer: u =. 9. ( pt) set/p-9.pg Given f (x) = 25sin(5x) and f (0) = 4 and f (0) = 5. Find f (π/5) = 0. ( pt) set/p-0.pg Given f (x) = 4x + 4 and f ( 3) = 5 and f ( 3) = 2. Find f (x) = and find f (2) =. ( pt) set/pr0.pg Find Z F(x) = Give a specific function for F(x). F(x) = x(x 2 + ) 3 dx +C.

16 2. ( pt) set/ns7 4 3.pg Find a function y of x such that 9yy = x and y(9) = 7. y = (function of x) 3. ( pt) set/ns7 4 0.pg Solve the separable differential equation 6x 2y x 2 + dy dx = 0 Subject to the initial condition: y(0) = 3 y = (function of x only) 2

17 Math 20-90, Fall 2007 WeBWorK Assignment 2 due /9/2008 at 0:59pm MST Introduction to Area; The Definite Integral This assignment will cover the material from Sections ( pt) set2/p0-4.pg If f(x) = R x 2 4 t2 dt then f (x) = f ( 2) = 2. ( pt) set2/sc pg Z 7 where a = and b = 3. ( pt) set2/pr3.pg Let Find and Z 0 9 Z 3 6 Z f (x)dx = 0, f (x)dx = Z 0 Z b f (x) f (x) = f (x) 9 a Z 6 9 (0 f (x) )dx = f (x)dx =, 4. ( pt) set2/ur in 0 2.pg Consider the function f (x) = x In this problem you will calculate the definition Z b a Z 0 Z ( x2 4 [ n f (x)dx = lim f (x i ) x n i= f (x)dx = 4. 2)dx by using ] The summation inside the brackets is R n which is the Riemann sum where the sample points are chosen to be the righthand endpoints of each sub-interval. Calculate R n for f (x) = x2 4 2 on the interval [0,4] and write your answer as a function of n without any summation signs. You will need the summation formulas on page 28 of your textbook. x i = 4i n and x = 4 n. (Show hint after attempts. ) R n = lim n R n = 5. ( pt) set2/osu in 0 5.pg The following sum + 3 n 3 n n + n n n + 3n n is a right Riemann sum for a certain definite integral Z b f (x)dx using a partition of the interval [,b] into n subintervals of equal length. Then the upper limit of integration must be: b = and the integrand must be the function f (x) = 3 n

18 Math 20-90, Fall 2008 WeBWorK Assignment 3 due /26/2008 at 0:59pm MST ; The First Fundamental Theorem of Calculus, The 2nd FTC and Substitution, the Integral Mean Value Theorem and Symmetry, and Numerical Integration This assignment will cover the material from Sections ( pt) set3/p-5.pg R s(s + )2 Evaluate the integral: ds. s Answer: + C. 2. ( pt) set3/p-6.pg Evaluate the indefinite integral: R 3y 2y dy. Answer: + C. 3. ( pt) set3/pr.pg Evaluate the indefinite integral. Z x 4 + x 5 dx 8. ( pt) set3/p0-5.pg Evaluate Z 4 I = x 2 x 3 + 0dx 0 I= 9. ( pt) set3/p0-6.pg Evaluate I= Z 7 I = 6 x (x 2 + ) 2 dx 0. ( pt) set3/sc5 8 5mod.pg Given the following integral and value of n, approximate the following integral using the methods indicated (round your answers to six decimal places): (a) Trapezoidal Rule Z (b) Simpson s (Parabolic) Rule 0 e 3x2 dx,n = 4 +C. 4. ( pt) set3/osu in 4 4.pg Evaluate the definite integral Z 2 ( d ) 3 + 2t dt 4 dt using the Fundamental Theorem of Calculus. You will need accuracy to at least 4 decimal places for your numerical answer to be accepted. You can also leave your answer as an algebraic expression involving square roots. Z 2 ( d ) 3 + 2t dt 4 dt = 5. ( pt) set3/p0-.pg Z 4 The value of (x + 6) 2 dx is 0 6. ( pt) set3/p0-2.pg Z 8 The value of dx is 6 x2 7. ( pt) set3/p0-3.pg Evaluate the definite integral Z 6 4x dx x. ( pt) set3/sc5 8 6mod.pg Use Simpson s Rule (the Parabolic Rule) and all the data in the Z following table to estimate the value of the integral ydx ( pt) set3/c4s4p2b.pg Z 7 If f (x) = t 8 dt x then f (x) = 3. ( pt) Z set3/c4s4pa.pg x If f (x) = (t 3 + 7t 2 + 5)dt 0 then f (x) = 4. ( pt) set3/c4s4p7.pg Given x y Z x f (x) = 0 t cos 2 (t) dt At what value of x does the local max of f (x) occur? x =

19 5. ( pt) set3/ur in 4 2.pg NOTE: It will be easier to see the function f(x) if you use the display mode typeset. Keep in mind, though, that loading the problem into your computer using this display mode will take longer. Let 0 if x < 3 5 if 3 x < f (x) = 3 if x < 4 0 if x 4 and Z x g(x) = f (t)dt 3 Determine the value of each of the following: (a) g( 6) = (b) g( 2) = (c) g(0) = (d) g(5) = (e) The absolute maximum of g(x) occurs when x = and is the value It may be helpful to make a graph of f(x) when answering these questions. 6. ( pt) set3/sc5 4 4.pg Use part I of the Fundamental Theorem of Calculus to find the derivative of Z 4 F(x) = sin(t 5 )dt x F (x) = [NOTE: Enter a function as your answer.] 7. ( pt) set3/sc5 4 8.pg Use part I of the Fundamental Theorem of Calculus to find the derivative of Z sin(x) h(x) = (cos(t 2 ) +t) dt 4 h (x) = [NOTE: Enter a function as your answer. Make sure that your syntax is correct, i.e. remember to put all the necessary *, (, ), etc. ] 8. ( pt) set3/osu in 4 3.pg Find the derivative of the following function Z x 5 F(x) = (2t )3 dt x 3 using the Fundamental Theorem of Calculus. F (x) = 9. ( pt) set3/ur in 4.pg Find a function f and a number a such that Z x 2 + a f (t) t 2 dt = 6x 2 There are two ways to solve this problem. The first (and better) way is to differentiate both sides of the above equation using the Fundamental Theorem of Calculus (Part I) on the integral. This will give an equation that can be solved for f(x). The value of the number a can be determined by normal integration (i.e. the Evaluation Theorem) of the original equation. The second way (and a bit harder) is to simply guess the form of f(x) and do normal integration to see if you are right. The value of the number a is determined as in the preceding paragraph above. (Show hint after attempts. ) f (x) = a = 2

20 Math 20-90, Fall 2008 WeBWorK Assignment 4 due 2/03/2008 at 0:59pm MST The Area of a Plane Region, Volumes of Slabs and Solids of Revolution: Disks, Washers This assignment will cover the material from Sections ( pt) set4/p3-.pg Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y = x 4 y = 64x about the x-axis. 2. ( pt) set4/p3-2.pg A ball of radius 2 has a round hole of radius 6 drilled through its center. Find the volume of the resulting solid. 3. ( pt) set4/p3-3.pg Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 3x 2,x =,y = 0, about the x-axis 7. ( pt) set4/p0-9.pg Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. x + y 2 = 30,x + y = 0 8. ( pt) set4/p0-0.pg Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. y = 7cosx,y = (2sec(x)) 2,x = π/4,x = π/4 9. ( pt) set4/p2-.pg Find the volume of the solid generated by revolving about the x-axis the region bounded by the upper half of the ellipse x 2 a 2 + y2 b 2 = and the x-axis, and thus find the volume of a prolate spheroid. Here a and b are positive constants, with a > b. 4. ( pt) set4/p3-6.pg Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 0,y = x(8 x) about the axis x = 0 Volume of the solid of revolution:. 0. ( pt) set4/p2-2.pg The region bounded by y = 2 + sinx, y = 0, x = 0 and 2π is revolved about the y-axis. Find the volume that results. Hint: Z xsinx dx = sinx xcosx +C. 5. ( pt) set4/p0-7.pg Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. y = 7x,y = 6x 2 6. ( pt) set4/p0-8.pg Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. y = 7x 2,y = x Volume of the solid of revolution:.. ( pt) set4/p3-5.pg Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x 4, y = 0, x = 2, x = 6; about the y-axis

21 Math 20-90, Fall 2008 WeBWorK Assignment 5 due 2/0/2008 at 0:59pm MST Length of a Plane Curve, Work and Fluid Force; Moments, Center of Mass; Probability and Random Variables This assignment will cover the material from Sections ( pt) set5/p2-3.pg Consider the parametric curve given by the equations x(t) = t 2 + 3t 45 y(t) = t 2 + 3t 20 How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=2? 2. ( pt) set5/p2-4.pg Find the area of the surface generated by revolving the following curve about the x-axis: x = r cost,y = r sint,0 t π, where r is a constant. 7. ( pt) set5/p3-2.pg A force of 3 pounds is required to hold a spring stretched 0.4 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.7 feet beyond its natural length? 8. ( pt) set5/p3-3.pg For a certain type of nonlinear spring, the force required to keep the spring stretched a distance s is given by the formula F = ks 4/3. If the force required to keep it stretched 8 inches is 2 pounds, how much work is done in stretching this spring 27 inches? Amound of work done: inch-pound(s). 9. ( pt) set5/p3-4.pg Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x 2,y = 0,x = 0,x = 2, about the y-axis Area of the surface:. 3. ( pt) set5/p2-5.pg The circle x = acost,y = asint,0 t 2π is revolved about the line x = b, 0 < a < b, thus generating a torus (doughnut). Find its surface area. Area of the torus:. 4. ( pt) set5/p2-6.pg Consider the parametric equation x = 5(cosθ + θsinθ) y = 5(sinθ θcosθ) What is the length of the curve for θ = 0 to θ = 8 π? 5. ( pt) set5/p2-7.pg If f (θ) is given by: f (θ) = 8cos 3 θ and g(θ) is given by: g(θ) = 8sin 3 θ Find the total length of the astroid described by f (θ) and g(θ). (The astroid is the curve swept out by ( f (θ),g(θ)) as θ ranges from 0 to 2π. ) 6. ( pt) set5/p3-.pg The force on a particle is described by 2x 3 6 at a point x along the x-axis. Find the work done in moving the particle from the origin to x = ( pt) set5/p3-6.pg A tank in the shape of an inverted right circular cone has height 2 meters and radius 7 meters. It is filled with 7 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is δ = 450kg/m 3 Work = Joules. (Note, use a value of g = 9.8m/s 2.). ( pt) set5/p3-7.pg Find the x-coordinate of the centroid of the region bounded by the following curves: y = x 2,y = x + 6. Hint: Make a sketch and use symmetry where possible. x-coordinate of Centroid:. 2. ( pt) set5/p3-8.pg A cylinder of radius 7 and depth 20 is filled with silver ore. The cost of extracting the ore lying at a depth of h feet is 20( +.03h 2 ) dollars per cubic foot. How much will it cost to empty the entire cylinder?

22 3. ( pt) set5/ur pb 7.pg Determine whether the following are valid probability distributions or not. Type VALID if it is valid, or type INVALID if it is not a valid probability distributions. (a) x P(x) answer: (b) P(x) = 3x, where x =,2,3,... answer: (c) answer: 4. ( pt) set5/ur pb 7 3.pg x P(x) x P(x) Given the discrete probability distribution above, determine the following: (a) P(x 2 or x < 9) = (b) P(x = 20) = (c) P(8 x < 20) = 5. ( pt) set5/ur pb 5 3.pg The density function of X is given by { a + bx 2 if 0 x f (x) = 0 otherwise If the expectation of X is E(X) = 0.575, find a and b. a = b = 2

23 Math 20-90, Fall 2008 WeBWorK Assignment 3 due 2/2/2008 at 0:59pm MST Real Numbers; Estimation, Inequalities; Roots. This assignment will cover the material from sections 0.-3 of the text.. ( pt) set3/srw 2 26.pg Evaluate the expression 8 4/3. [NOTE: Your answer cannot be an algebraic expression. ] 2. ( pt) set3/srw 2 60.pg ( ) The expression x 2 y 4 z 2 x 5 4 x 5 y 2 z 4 y equals x r y s z t 5 where r, the exponent of x, is: and s, the exponent of y, is: and finally t, the exponent of z, is: [NOTE: Your answers cannot be algebraic expressions.] 3. ( pt) set3/srw 2 9.pg The expression 3 64x 5 equals nx r where n, the leading coefficient, is: and r, the exponent of x, is: [NOTE: Your answers cannot be algebraic expressions.] 4. ( pt) set3/srw 2 09.pg If you rationalize the denominator of then you will get r 5 + s 3 n where r, s, and n are all positive integers (with no common factors). r = s = n = [NOTE: Your answers cannot be algebraic expressions.] 5. ( pt) set3/ur ab 7 2.pg Consider the inequality x 2 < 5x + 4 The solution of this inequality consists one or more of the following intervals: (,A), (A,B), and (B, ) where A < B. Find A Find B For each interval, answer YES or NO to whether the interval is included in the solution. (, A) (A,B) (B, ) 6. ( pt) set3/ur ab 7 4.pg Consider the inequality x + 2 x + 9 < 3 The solution of this inequality consists one or more of the following intervals: (, A), (A, B),and (B, ) where A < B. Find A Find B For each interval, answer YES or NO to whether the interval is included in the solution. (, A) (A,B) (B, ) 7. ( pt) set3/srw 8.pg Match the statements defined below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit.. x 2 = 9 2. x 2 < 3. x 2 > 9 4. x x 2 9 A. x (, 7) (, ) B. x (, 7] [, ) C. x (, ) D. x { 7,} E. x [ 7,] 8. ( pt) set3/srw 8 23.pg To say that x 8 2 is the same as saying x is in the closed interval [A,B] where A is: and where B is: 9. ( pt) set3/srw 8 26.pg To say that x is the same as saying x is in the closed interval [A,B] where A is: and where B is: 0. ( pt) set3/srw 8 29.pg To say that x is the same as saying x is in the closed interval [A,B] where A is: and where B is:

24 Math 20-90, Fall 2008 WeBWorK Assignment 4 due 2/2/2008 at 0:59pm MST Rectangular Coordinates, Graphs, Lines; Functions and Their Graphs; Operations on Functions; The Trigonometric Functions. This assignment will cover the material from sections of the text.. ( pt) set4/s0 2.pg Let f (x) = 3x 2 f (+h) f () + 3x + 5 and let g(h) = h. Determine each of the following: (a) g() = (b) g(0.) = (c) g(0.0) = You will notice that the values that you entered are getting closer and closer to a number L. This number is called the limit of g(h) as h approaches 0 and is also called the derivative of f(x) at the point when x =. We will see more of this when we get to the calculus textbook. Enter the value of L: 2. ( pt) set4/s0 0.pg The domain of the function f (x) = 4x 4 22 is all real numbers x except for x where x equals 3. ( pt) set4/s0 8.pg The domain of the function f (x) = x 2 2x + 27 consists of one or more of the following intervals: (,A], [A,B] and [B, ) where A < B. Find A Find B For each interval, answer YES or NO to whether the interval is included in the solution. (, A] [A,B] [B, ) 4. ( pt) set4/s pg For each of the following functions, decide whether it is even, odd, or neither. Enter E for an EVEN function, O for an ODD function and N for a function which is NEITHER even nor odd. NOTE: You will only have four attempts to get this problem right!. f (x) = x 2 6x 2 + 3x 2 2. f (x) = 5x 2 3x f (x) = x 6 4. f (x) = x 2 + 3x 2 + 2x 5 5. ( pt) set4/s0 84a.pg Let f (x) = 2x + 4 and g(x) = 3x 2 + 5x. After simplifying, ( f g)(x) = 6. ( pt) set4/c0sp/c0sp.pg The simplest functions are the linear (or affine) functions the functions whose graphs are a straight line. They are important because many functions (the so-called differentiable functions) locally look like straight lines. ( locally means that if we zoom in and look at the function at very powerful magnification it will look like a straight line.) Enter the letter of the graph of the function which corresponds to each statement.. The graph of the line is increasing 2. The graph of the line is decreasing 3. The graph of the line is constant 4. The graph of the line is not the graph of a function A B C D 7. ( pt) set4/c0sp3/c0sp3.pg Almost any kind of quantitative data can be represented by a graph and most of these graphs represent functions. This is why functions and graphs are the objects analyzed by calculus. The next two problems illustrate data which can be represented by a graph. Match the following descriptions with their graphs below:. The graph of the velocity of a car as it drives along a city street vs. time. 2. The graph of the distance traveled by a car as it drives along a city street vs. time. 3. The graph of the velocity of a car entering a superhighway vs. time. 4. The graph of the distance traveled by a car as it enters a superhighway vs. time.

25 A B C D 8. ( pt) set4/c0sp4/c0sp4.pg Match the following descriptions with their graphs below:. The graph of the number of days until next Friday vs. time. 2. The graph of the amount of time until midnight next Friday as a function of time. 3. The graph of the number of days to the nearest Friday (in the future or in the past) as a function of time. 4. The graph of the amount of time to the nearest Friday at midnight vs. time. A B C D 9. ( pt) set4/c0sp8a/c0sp8a.pg. The interval from a to b 2. The interval from b to c 3. The interval from c to d 4. The interval from d to e 5. The interval from e to f A. The car is in front of the starting line on this interval B. The car is behind the starting line on this inteval. C. The velocity of the car is positive on this interval. D. The velocity of the car is negative on this interval. E. The displacement of the car from the starting line is increasing on this interval. F. The displacement of the car from the starting line is decreasing on this interval. The function to the left represents the displacement of a toy race car as it travels a linear track. Negative numbers mean the car is behind the starting line, positive numbers mean it is in front. Postive velocities mean it is moving forward, while negative velocities mean it is moving backwards. Remember that a value which changes from -2 to - to 0 is increasing! For each interval, enter all letters whose corresponding statements are true for that interval ( pt) set4/c0s5p3.pg Determine which of the following statements are true and which are false. Enter the T or F in front of each statement. Remember that x (,) is the same as < x < and x [,] means x.. The function sin(x) on the domain x [ π/2,π/2] has at least one input which produces a largest output value. 2. The function f (x) = x 2 with domain x [ 3,3] has at least one input which produces a largest output value. 3. The function f (x) = x 2 with domain x ( 3,3) has at least one input which produces a largest output value.

26 4. The function f (x) = x 2 with domain x [ 3,3] has at least one input which produces a smallest output value. 5. The function sin(x) on the domain x ( π/2,π/2) has at least one input which produces a smallest output value.. ( pt) set4/ns 9.pg Let f (x) = 3x 2 + x 2. Find f (0) f () f (3) f ( 3) f ( + 3) 2. ( pt) set4/ur fn 2.pg Let f be the linear function (in blue) and let g be the parabolic function (in red) below. If you are having a hard time seeing the picture clearly, click on the picture. It will expand to a larger picture on its own page so that you can inspect it more closely. 3. g f 4. f g A. 25x + 30 B. 75x x + 00 C. 5x x + 5 D. 27x x x x 4. ( pt) set4/c0sp9.pg This problem gives you some practice identifying how more complicated functions can be built from simpler functions. Let f (x) = x 3 27and let g(x) = x 3. Match the functions defined below with the letters labeling their equivalent expressions.. g(x 2 ) 2. ( f (x)) 2 3. f (x)/g(x) 4. g(x) f (x) A x 3 + x 6 B. 3 + x 2 C x + x 2 D. 8 27x 3x 3 + x 4 5. ( pt) set4/c0s2p3.pg Relative to the graph of y = f (x) the graphs of the following equations have been changed in what way?. y = f (x/7) 2. y = f (x) 7 3. y = f (x + 7) 4. y = 7 f (x) A. stretched horizontally by the factor 7 B. stretched vertically by the factor 7 C. shifted 7 units left D. shifted 7 units down Note: If the answer does not exist, enter DNE :. (f o g)( 2 ) = 2. (g o f)( 2 ) = 3. (f o f)( 2 ) = 4. (g o g)( 2 ) = 5. (f + g)( 4 ) = 6. (f / g)( 2 ) = 6. ( pt) set4/c0s2p2/c0s2p2.pg This is a graph of the function F(x): (Click on image for a larger view ) 3. ( pt) set4/s0 87.pg Let f (x) = 5x + 5 and g(x) = 3x 2 + 5x. Match the statements defined below with the letters labeling their equivalent expressions. You must get all of the answers correct to receive credit.. f f 2. g g 3

27 Enter the letter of the graph below which corresponds to the transformation of the function.. F(x 3) 2. 5F(x) 3. F(x + 3) 4. F( x) A B C D 7. ( pt) set4/ur tr 4.pg Convert 3 4π to degrees: Convert 38 to radians: π 8. ( pt) set4/ur tr 5.pg Evaluate the following expressions sin( π 6 ) cos(π) tan( 4π 3 ) cot( π 2 ) sec( π 4 ) csc( 2π 3 ) 9. ( pt) set4/ur tr 6.pg If θ = 3π 4, then sin(θ) equals cos(θ) equals tan(θ) equals sec(θ) equals 20. ( pt) set4/ur tr 2a.pg For 0 < θ < π/2, find the values of the trigonometric functions based on the given one (give your answers with THREE DECI- MAL PLACES or as fractions, e.g. you can enter 3/5). If sec(θ) = 6 then csc(θ)= sin(θ) = cos(θ) = tan(θ) = cot(θ) = 4

28 WeBWorK demonstration assignment The main purpose of this WeBWorK set is to familiarize yourself with WeBWorK. Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK change your password. Find out how to print a hard copy on the computer system that you are going to use. Print a hard copy of this assignment. Get to work on this set right away and answer these questions well before the deadline. Not only will this give you the chance to figure out what s wrong if an answer is not accepted, you also will avoid the likely rush and congestion prior to the deadline. The primary purpose of the WeBWorK assignments in this class is to give you the opportunity to learn by having instant feedback on your active solution of relevant problems. Make the best of it!. ( pt) setdemo/demo pr.pg Evaluate the expression 5(8 5) =. 2. ( pt) setdemo/demo pr2.pg Evaluate the expression 8/(3 + ) =. Enter you answer as a decimal number listing at least 4 decimal digits. (WeBWorK will reject your answer if it differs by more than one tenth of percent from what it thinks the answer is.) 3. ( pt) setdemo/demo pr3.pg Let r = 7. Evaluate 4/π r =. Next, enter the expression 4/(π r) = WorK compute the result. 4. ( pt) setdemo/demo pr4.pg Enter here the expression a + b. Enter here the expression a+b. 5. ( pt) setdemo/demo pr5.pg Enter here the expression a b Enter here the expression a + b c + d and let WeB- If WeBWorK rejects your answer use the preview button to see what it thinks you are trying to tell it. 6. ( pt) setdemo/demo pr6.pg Enter here the expression a + b Enter here Enter here 7. ( pt) setdemo/demo pr7.pg Enter here Enter here Enter here 8. ( pt) setdemo/demo pr8.pg Enter here a a + b a + b a + b x 2 + y 2 x x 2 + y 2 the expression the expression the expression the expression the expression x + y x 2 + y 2 b + b 2 4ac 2a the expression Note: this is an expression that gives the solution of a quadratic equation by the quadratic formula. 9. ( pt) setdemo/demo pr9.pg Simplify the expression sin 2 (x) 0. ( pt) setdemo/demo pr0.pg Evaluate the expression ( )