WeBWorK demonstration assignment

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) Evaluate the it x 3 x 3 x 6x 7.( pt) Evaluate the it x x x 3.( pt) Evaluate the it x.( pt) Evaluate x 0 x 0 6x 3 x 6 0x x x x 5.( pt) Let f t t 5t 3 t 5. (a) f t (b) f [NOTE: Your answer to part (a) should be a function in terms of the variable t and not a number! Your answer to part (b) should be a number.] 6.( pt) If f x x x 8 x x, find f y. 7.( pt) If 5x x xy 30 and y 5 3, find 5 by implicit differentiation. 8.( pt) Use implicit differentiation to find the slope of the tangent line to the curve at the point 7. m 9.( pt) Let f x f x xy 3 xy 9sin sin x 3 0.( pt) Consider the function f x 7x 3 x. The absolute maximum value is and this occurs at x equals The absolute minimum value is and this occurs at x equals.( pt) Consider the function f x x 3 8x 6x 3 9 x. This function has an absolute minimum value equal to and an absolute maximum value equal to.( pt) For x 3 the function f is defined by f x x 5 x On which two intervals is the function increasing (enter intervals in ascending order)? to and to Find the region in which the function is positive: to Where does the function achieve its minimum? 3.( pt) If 00 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = cubic centimeters..( pt) A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle.

What is the area of the largest possible Norman window with a perimeter of feet? 5.( pt) Evaluate the definite integral 9 6x 9 dx x 6.( pt) Evaluate the definite integral 3 9 7 x dx 7.( pt) The velocity function is v t t 6t 8 for a particle moving along a line. Find the displacement (net distance covered) of the particle during the time interval [-,6]. displacement = 8.( pt) Consider the function f x x if x x if x Evaluate the definite integral. f x dx 3 9.( pt) Find the area between the curves: y x 3 x x and y x 3 x x 0.( pt) The total area enclosed by the graphs of y 5x x 3 x y x x is.( pt) Consider the parametric curve given by the equations x t t 9t y t t 9t 9 How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=5?.( pt) A ball is shot straight up into the air with initial velocity of 0 ft/sec. Assuming that the air resistance can be ignored, how high does it go? Hint: The acceleration due to gravity is 3 ft per second squared. 3.( pt) A stone is thrown straight up from the edge of a roof, 65 feet above the ground, at a speed of 8 feet per second. A. Remembering that the acceleration due to gravity is -3 feet per second squared, how high is the stone seconds later? B. At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground?

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) The point P 3 5 lies on the curve y x x 3. If Q is the point x x x 3, find the slope of the secant line PQ for the following values of x. If x 3, the slope of PQ is: and if x 3 0, the slope of PQ is: and if x 9, the slope of PQ is: and if x 99, the slope of PQ is: Based on the above results, guess the slope of the tangent line to the curve at P 3 5..( pt) A particle moves along a straight line and its position at time t is given by s t t 3 t t where s is measured in feet and t in seconds. Find the velocity (in ft/sec) of the particle at time t 0: The particle stops moving (i.e. is in a rest) twice, once when t A and again when t B where A B. A is and B is What is the position of the particle at time 6? Finally, what is the TOTAL distance the particle travels between time 0 and time 6? 3.( pt) The population of a slowly growing bacterial colony after t hours is given by p t 5t t 00. Find the growth rate after hours..( pt) A particle moves along a straight line with equation of motion s t 3t 3 Find the value of t (other than 0 ) at which the acceleration is equal to zero. 5.( pt) Let f x x 3x 3 6x 3x. Then f x is and f is f x is and f is 6.( pt) Let f x x 7 3x 5 5x 3 x. Then f x is f 5 is f x is and f 5 is 7.( pt) If f x 5x 8 5x 5 5x 3 6x, find f 5. 5. 8.( pt) If g t g 0 t 6t find g 0 g 0 g 0 g 0 g 5 0 9.( pt) Consider the function f x x 3 5x 6x 9. Enter an antiderivative of f x 0.( pt) Consider the function f x 0x 3 9x x. An antiderivative of f x is F x Ax Bx 3 Cx Dx where A is and B is and C is and D is.( pt) Consider the function f x x 9 3x 5 7x 5. Enter an antiderivative of f x

.( pt) Consider the function f x 9x 8 7x 6 x 8. An antiderivative of f x is F x Ax n Bx m Cx p Dx q where A is and n is and B is and m is and C is and p is and D is and q is 3.( pt) Given and f f x x 5 3 and f 3 5. x and find f 3.( pt) A car traveling at ft/sec decelerates at a constant 7 feet per second squared. How many feet does the car travel before coming to a complete stop? 5.( pt) A ball is shot straight up into the air with initial velocity of 5 ft/sec. Assuming that the air resistance can be ignored, how high does it go? Hint: The acceleration due to gravity is 3 ft per second squared.

Tom Robbins WW Prob Lib Math 0-00, Spring 00 WeBWorK problems. WeBWorK assignment due /8/0 at :59 PM..( pt) 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. 5.( pt) Let f 6.( pt) Let f x x x 9 f x x 5 x 8 The domain of f is the interval A B where A and where B 7.( pt) For each of the following angles, find the degree measure of the angle with the given radian measure: 6 5 5 3 Note: If the answer does not exist, enter DNE :. (f o g)( ) =. (g o f)( ) = 3. (f o f)( ) =. (g o g)( ) = 5. (f + g)( ) = 6. (f / g)( ) =.( pt) If f is one-to-one and f 9 5, then f 5 and f 9. If g is one-to-one and g 3 0, then g 0 and g 3. If h is one-to-one and h h 9 and h 3.( pt) If f x x, then f y f 6.( pt) If f x x x 0, then f 7 9, then 3 8.( pt) For each of the following angles, find the radian measure of the angle with the given degree measure (you can enter as pi in your answers): 30 90 300 30 60 9.( pt) For each of the followings angles (in radian measure), find the sin of the angle (your answer cannot contain trig functions, it must be an arithmetic expression or number): 6 3 0.( pt) For each of the followings angles (in radian measure), find the cos of the angle (your answer cannot contain trig functions, it must be an arithmetic expression or number): 6 3

.( pt) If θ, then sin θ equals cos θ equals tan θ equals sec θ equals.( pt) If θ 7 6, then sin θ equals cos θ equals tan θ equals sec θ equals 3.( pt) The angle of elevation to the top of a building is found to be from the ground at a distance of 000 feet from the base of the building. Find the height of the building..( pt) 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 9. From a point 000 feet closer to the mountain along the plain, they find that the angle of elevation is 3. How high (in feet) is the mountain? 5.( pt) Let F be the function 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 clearly. Evaluate each of the following expressions. Note: Enter DNE if the it does not exist or is not defined. a) x F x = b) x F x = c) x F x = d) F = e) x F x = f) x F x = g) x F x = h) x 3F x = i) F 3 = 6.( pt) Evaluate the it x x x 8x 9 7.( pt) Evaluate the it a 3 a a

Tom Robbins WW Prob Lib Math 0-00, Spring 00 WeBWorK problems. WeBWorK assignment 3 due 3//0 at :59 PM..( pt) Evaluate the it x 5x 3 8 5.( pt) Evaluate the it x 7 x 3 6x 7x 7 3.( pt) Evaluate the it x x x 5x 36.( pt) Evaluate the it a 3 a a 5.( pt) Evaluate the it t t 5 5 t 5 6.( pt) Let f x 3 if x 8, f x 7 if x 8, f x x 0 if 9 x 8, f x 9 if x 9. Sketch the graph of this function and find following its if they exist (if not, enter DNE).. x 8 f x. x 8 f x 3. x 8 f x. x 9 f x 5. x 9 f x 6. x 9 f x 7.( pt) Evaluate the it 5x x 7 7x 8.( pt) Evaluate the it 0x x 9x x 3 9.( pt) Evaluate the it x 3 8x x x 9 8x 0x 3 0.( pt) Evaluate the it x x 3 7x.( pt) Evaluate the it x 8 x 9 8x x 9 8x.( pt) Evaluate 8t 9 t t t 5 3.( pt) Evaluate the following its. If needed, enter INF for and MINF for. (a) (b) x 3x 6 x 9x 6 3x x 6 x 9x 6.( pt) Evaluate the following its. If needed, enter INF for and MINF for. (a) 5 x x 7 0x (b) 5 x x 7 0x 5.( pt) Enter a letter and a number for each formula below so as to define a continuous function.

The letter refers to the list of equations and the number is the value of the function f at. Letter Number A. x x when x x x 5 x when x cos x x when x x x when x x 3 x when x sin x B. x when x C. x 3 7 when x D. when x 6.( pt) The function f is given by the formula f x 3 x 0x 8x x 6 when x 6 and by the formula f x x 3x a when 6 x. What value must be chosen for a in order to make this function continuous at 6? a = 7.( pt) Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false. A statement is true only if it is true for all possibilities. You must get all of the answers correct to receive credit.. If f x 0 and g x, then x x x f x g x does not exist x x 3. x x 7x 8 x x x 3 x x 7x 8 3. If f x is differentiable at a, then f x is continuous at a. If f x is continuous at a, then f x is differentiable at a 5. If f x g x exists, then the it is x 6 f 6 g 6 8.( pt) If f x 5, find f. 9.( pt) If f x 5x, find f 0.( pt) If f x 3 x 5x, find f.( pt) If f x, find f 5. x.( pt) Let f 3.( pt) Let f x 3 x 6. 5. f x x Use the it definition of the derivative on page 56 to find (i) f 5 (ii) f (iii) f 0 (iv) f 3 To avoid calculating four separate its, I suggest that you evaluate the derivative at the point when x a. Once you have the derivative, you can just plug in those four values for a to get the answers.

y y 3.( pt) Let f x f x 5x 6 3x 6.( pt) If x x xy 8 and y 3, find 3 by implicit differentiation. 5.( pt) If x 6 and y 7 6665, find by implicit differentiation. 9 y 6.( pt) Use implicit differentiation to find the slope of the tangent line to the curve 3x 3xy y 3 at the point 3. m 7.( pt) Use implicit differentiation to find the equation of the tangent line to the curve xy 3 xy 6 at the point 8. The equation of this tangent line can be written in the form y mx b where m is: and where b is: 8.( pt) Find y by implicit differentiation. Match the expressions defining y implicitly with the letters labeling the expressions for y.. 5cos x y 3ysinx. 5sin x y 3ysinx 3. 5cos x y 3ycosx. 5sin x y 3ycosx A. 5sin x y 3ysin x 3cos x 5sin x y B. 5sin x y 3ycos x C. D. 3sinx 5sin x y 5cos x y 3ycos x 5cos x y 3sin x 5cos x y 3ysin x 5cos x y 3cos x 9.( pt) At noon, ship A is 0 nautical miles due west of ship B. Ship A is sailing west at 8 knots and ship B is sailing north at 5 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: knot is a speed of nautical mile per hour.) 0 0.( pt) Gravel is being dumped from a conveyor belt at a rate of 0 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 0 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V 3 r h..( pt) A street light is at the top of a ft tall pole. A woman 6 ft tall walks away from the pole with a speed of ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?.( pt) Use linear approximation, i.e. the tangent line, to approximate 9 as follows: Let f x x. The equation of the tangent line to f x at x 9 can be written in the form y mx b where m is: and where b is: Using this, we find our approximation for 9 is NOTE: For this part, give your answer to at least 9 significant figures or use fractions to give the exact answer. 3.( pt) Use linear approximation, i.e. the tangent line, to approximate 7 3 as follows: Let f x x 3. The equation of the tangent line to f x at x can be written in the form y mx b where m is: and where b is: Using this, we find our approximation for 7 3 is.( pt) Suppose that you can calculate the derivative of a function using the formula f x f x x. If the output value of the function at x is 3 estimate the value of the function at 0.

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) The function f x x 3 39x 6x 8 has two critical numbers. The smaller one equals and the larger one equals.( pt) Consider the function f x 3 3x 5 x. The absolute maximum value is and this occurs at x equals The absolute minimum value is and this occurs at x equals 3.( pt) The function f x x 3 x 36x 7 has one local minimum and one local maximum. This function has a local minimum at x equals with value and a local maximum at x equals with value.( pt) Consider the function f x 5x 8x 8. f x is increasing on the interval A and decreasing on the interval A where A is the critical number. Find A At x A, does f x have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER. 5.( pt) Consider the function f x x 5 30x 300x 3 7. For this function there are four important intervals: A, A B, B C, and C where A, B, and C are the critical numbers. Find A and B and C At each critical number A, B, and C does f x have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER. At A At B At C 6.( pt) For x the function f is defined by f x x 6 7 x 3 On which two intervals is the function increasing? to and to Find the region in which the function is positive: to Where does the function achieve its minimum? 7.( pt) Consider the function f x x 8x. 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 : 8.( pt) Answer the following questions for the function f x x x 6 defined on the interval 7 6. 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 9.( pt) Answer the following questions for the function f x x x 8x 5 x 8x 5 defined on the interval 9 0. 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 0.( pt) A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y x. What are the dimensions of such a rectangle with the greatest possible area? Width = Height =.( pt) A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 8. What are the dimensions of such a cylinder which has maximum volume? Radius = Height =.( pt) A rancher wants to fence in an area of 500000 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?

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) Consider the function f x x 3 6x x. Enter an antiderivative of f x.( pt) Consider the function f x 8x 3 3x 8x 6. An antiderivative of f x is F x Ax Bx 3 Cx Dx where A is and B is and C is and D is 8 3.( pt) Consider the function f x. x x 7 Let F x be the antiderivative of f x with F 0. Then F x.( pt) Consider the function f x whose second derivative is f x 3x 6sin If f 0 and f 0, what is f x? 5.( pt) A ball is shot straight up into the air with initial velocity of ft/sec. Assuming that the air resistance can be ignored, how high does it go? Hint: The acceleration due to gravity is 3 ft per second squared. 6.( pt) A ball is shot at an angle of 5 degrees into the air with initial velocity of 8 ft/sec. Assuming no air resistance, how high does it go? How far away does it land? Hint: The acceleration due to gravity is 3 ft per second squared. 7.( pt) A stone is thrown straight up from the edge of a roof, 65 feet above the ground, at a speed of 8 feet per second. A. Remembering that the acceleration due to gravity is -3 feet per second squared, how high is the stone seconds later? B. At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground? 8.( pt) A stone is dropped from the edge of a roof, and hits the ground with a velocity of -5 feet per second. How high (in feet) is the roof? 9.( pt) Evaluate the it using L Hospital s rule if necessary sin 9x x 0 sin 7x 0.( pt) Evaluate the it using L Hospital s rule sin x x 0 tan x.( pt) Evaluate the it x x 3x 3 x.( pt) Compute the following it using l Hôpital s rule if appropriate. Use INF to denote and MINF to denote. 3 x x 3 x x =

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) Consider the differential equation: du dt u3 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 at t 0. Answer: u..( pt) An object is moving along a coordinate line subject to acceleration a (in centimeters per second per second) as follows a t with initial velocity v 0 0 (in centimeters per second) and directed distance s 0 0 (in centimeters). Find both the velocity v and the directed distance s after seconds. Velocity after seconds: centimeter(s) per second. Directed distance after seconds: centimeter(s). 3.( pt) The wolf population P in a certain state has been growing at a rate proportional to the cube root of the population size. The population was estimated at 000 in 980 and at 700 in 990. a) Find the differential equation for P t and the corresponding conditions. (Instruction: Use C for the constant of proportionality.) dp dt = P and P b) Solve your differential equation. P. c) When will the wolf population reach 000? The population will reach 000 by the year..( pt) Find 6 k k sin k =. 5.( pt) Find the value of the following collapsing sum: 0 k k k =. 6.( pt) Use the Special Sum Formulas (see Section 5.3 of Varberg, Purcell and Rigdon) to find: 0 i i i 3 =. 7.( pt) In statistics, we define the mean x and the variance s of a sequence of numbers x x n by x n n i x i. s x i x. n n i Find x and s for the sequence of numbers, 5, 7, 8, 9, 0,. x. s.

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) Find the indicated it. Make sure that you have an indeterminate form before you apply l Hopital s Rule. x 3 3x x x 0 x 3 =. x Instruction: If your answer is, enter Infinity ; if it is, enter -Infinity..( pt) Find the indicated it. Make sure that you have an indeterminate form before you apply l Hopital s Rule. x 0 sinx tanx =. x sinx Instruction: If your answer is, enter Infinity ; if it is, enter -Infinity. 3.( pt) Evaluate the integral: s s ds. s Answer: + C..( pt) Find: sin xdx. Answer: + C. 5.( pt) Consider the function f x whose second derivative is f x 3x sin If f 0 3 and f 0, what is f 3? 6.( pt) Consider the function f x 5x 8 5x 5 x 3 5. Enter an antiderivative of f x 7.( pt) Consider the differential equation: dy dx x y. a) Find the general solution to the above differential equation. (Instruction: Call your integration constant C.) Answer: y. b) Find the particular solution of the above differential equation that satisfies the condition y at x. Answer: y. 8.( pt) An object is moving along a coordinate line subject to acceleration a (in centimeters per second per second) as follows a t with initial velocity v 0 0 (in centimeters per second) and directed distance s 0 0 (in centimeters). Find both the velocity v and the directed distance s after seconds. Velocity after seconds: centimeter(s) per second. Directed distance after seconds: centimeter(s). 9.( pt) 0 f x 3 f x where a= and b= 0.( pt) Consider the integral 7 x dx 3 a b f x (a) Find the Riemann sum for this integral using right endpoints and n. (b) Find the Riemann sum for this same integral, using left endpoints and n.( pt) Compute the indefinite integral 5x 3 sec x tan x dx

.( pt) Evaluate the integral x 3 x 7 3 dx by making the substitution u x 7. NOTE: Your answer should be in terms of x and not u. 3.( pt) Evaluate the integral by making the given substitution. dx 8x 3 u 8x.( pt) Evaluate the indefinite integral. x 3 5 x dx 5.( pt) Evaluate the indefinite integral. cosx 5sinx 30 dx C