Assignment busshw1 due 10/15/2012 at 01:04pm EDT

Transcription

1 Administrator Assignment busshw1 due 10/15/2012 at 01:04pm EDT math (1 pt) Library/Rochester/setVectors0Introduction/ur vc 0 2.pg If the distance from the town of Bree to Weathertop is 6 miles on a 45 degree upward slope, what is the elevation gain (omit units)? (1 pt) Library/Rochester/setVectors0Introduction/ur vc 0 1.pg If Tom Bombadil s house is 5 miles east of Hobbiton and 12 miles south, what is the straight line distance (omit units)? (1 pt) Library/Rochester/setAlgebra14Lines/faris1.pg The demand equation for a certain product is given by p = x, where p is the unit price (in dollars) of the product and x is the number of units produced. The total revenue obtained by producing and selling x units is given by R = xp. Match the Lines L1 (blue), L2 ( red) and L3 (green) with the slopes by placing the letter of the slopes next to each set listed below: 1. The slope of line L1 2. The slope of line L3 3. The slope of line L2 A. m = 0.5 B. m = 0 C. m = 2 A C B 5. (1 pt) Library/Rochester/setAlgebra14Lines/lh2-1 5.pg Find an equation y = mx+b for the line whose graph is sketched Determine prices p that would yield a revenue of 6630 dollars. Lowest such price = Highest such price = (1 pt) Library/Rochester/setAlgebra14Lines/lh2-1 1 mo.pg The slope m equals. The y-intercept b equals (1 pt) Library/Rochester/setAlgebra14Lines/srw pg The equation of the line with slope 3 that goes through the point (5,5) can be written in the form y = mx + b where m is: and where b is: 1

2 (1 pt) Library/Rochester/setAlgebra14Lines/slope from pts var.pg Find the slope of the line passing through the points (a,2a 1) and (a + h,2(a + 3h) 1). The slope is 6 8. (1 pt) Library/Rochester/setAlgebra14Lines/sApB pg A line through ( 3,6) with a slope of 5 has a y-intercept at 1 9. (1 pt) Library/Rochester/setAlgebra14Lines/sw pg Find the slope and y-intercept of the line 6x + 4y = 0. the slope of the line is: the y-intercept of the line is: 13. (1 pt) Library/Rochester/setAlgebra14Lines/sw2 4 5.pg The equation of the line that goes through the points ( 5, 10) and (7,6) can be written in the form y = mx + b where its slope m is: (1 pt) Library/Rochester/setAlgebra14Lines/srw pg The equation of the line with slope 4 that goes through the point ( 9,4) can be written in the form y = mx + b where m is: and where b is: (1 pt) Library/Rochester/setAlgebra14Lines/sw pg Find an equation y = mx+b for the line whose graph is sketched (1 pt) Library/Rochester/setAlgebra14Lines/sApB 31-36a.pg An equation of a line through (4, 5) which is perpendicular to the line y = 4x + 3 has slope: and y-intercept at: (1 pt) Library/Rochester/setAlgebra14Lines/sw pg Find the slope and y-intercept of the line x + y = 5. the slope of the line is: the y-intercept of the line is: (1 pt) Library/Rochester/setAlgebra14Lines/sw pg The equation of the line that goes through the points (3,4) and (6,5) can be written in the form y = mx+b where m is: and b is: The number m equals. The number b equals (1 pt) Library/Rochester/setAlgebra14Lines/pts to gen.pg The equation of the line that goes through the points (3, 6) and ( 4,10) can be written in general form Ax + By +C = 0 where A = B = C =

3 (1 pt) Library/Rochester/setAlgebra14Lines/sApB pg An equation of a line through (1, 1) which is perpendicular to the line y = 2x + 1 has slope: and y-intercept at: The slope m equals. The y-intercept b equals (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh pg (1 pt) Library/Rochester/setAlgebra14Lines/srw pg The equation of the line with slope 4 that goes through the point (6, 2) can be written in the form y = mx + b where m is: and where b is: (1 pt) Library/Rochester/setAlgebra14Lines/srw a.pg The equation of the line that goes through the point (6,7) and is perpendicular to the line 3x + 5y = 5 can be written in the form y = mx + b where m is: and where b is: (1 pt) Library/Rochester/setAlgebra14Lines/lh2-1 9.pg Find an equation y = mx+b for the line whose graph is sketched The graph of a quadratic function f (x) is shown above. It has a vertex at ( 2, 4) and passes the point (0,0). Find the quadratic function. (x+2)** (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh pg Attention: you are allowed to submit your answer two times only for this problem! 3 Identify the graphs A (blue), B (red) and C (green):

4 is the graph of the function 4 x 2 is the graph of the function g(x) = 2 (x 6) 2 is the graph of the function h(x) = (x + 4) 2 6 C A B 24. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh pg Attention: you are allowed to submit your answer two times only for this problem! Identify the graphs A (blue), B (red) and C (green): is the graph of the function (x 5) 2 is the graph of the function g(x) = (x 2) 2 5 is the graph of the function h(x) = (x + 5) 2 2 C B A 26. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh pg The revenue function in terms of the number of units sold,x, is given as Identify the graphs A (blue), B (red) and C (green): is the graph of the function (x 5) 2 is the graph of the function g(x) = (x + 6) 2 is the graph of the function h(x) = x 2 5 A B C R = 380x 0.5x 2 where R is the total revenue in dollars. Find the number of units sold x that produces a maximum revenue? Your answer is x = What is the maximum revenue? (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh pg Attention: you are allowed to submit your answer two times only for this problem! (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh pg

5 Note: right. Be careful, You only have TWO chances to get them 1. x + 7 = y x = y 2 3. x 2 + 5y = x = y 3 The graph of a quadratic function f (x) is shown above. It has a vertex at (2,0) and passes the point (0,8). Find the quadratic function. *(x-2)**2 28. (1 pt) Library/Rochester/setAlgebra20QuadraticFun/lh pg 30. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/c0s5p4.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 ( 1,1) is the same as 1 < x < 1 and x [ 1,1] means 1 x The function sin(x) on the domain x ( π,π) has at least one input which produces a smallest output value. 2. The function sin(x) on the domain x [ π,π] has at least one input which produces a largest output value. 3. The function sin(x) on the domain x [ π,π] has at least one input which produces a smallest output value. 4. The function x 3 with domain x [ 3,3] has at least one input which produces a smallest output value. 5. The function x 3 with domain x ( 3,3) has at least one input which produces a smallest output value. The graph of a quadratic function f (x) is shown above. It has a vertex at (1,2) and passes the point (0,1). Find the quadratic function. T T T T F -(x-1)** (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/2.pg Enter Yes or No in each answer space below to indicate whether the corresponding equation defines y as a function of x (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/lh2-3 30a.pg

6 Consider the function whose graph is sketched: 33. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/lh2-3 48a.pg Consider the function whose graph is sketched: Find the intervals over which the function is strictly increasing or decreasing. Express your answer in interval notation. The interval over which the function is strictly increasing: The interval over which the function is strictly decreasing: [3,infinity) (-infinity,3] Find the intervals over which the function is strictly increasing or strictly decreasing. Express your answer in interval notation. The interval over which the function is strictly increasing: 32. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/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 ( 1,1) is the same as 1 < x < 1 and x [ 1,1] means 1 x The function sin(x) on the domain x ( π/2,π/2) has at least one input which produces a smallest output value. 2. The function x 2 with domain x [ 3,3] has at least one input which produces a largest output value. 3. The function sin(x) on the domain x [ π/2,π/2] has at least one input which produces a smallest output value. 4. The function 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 largest output value. F T T T F 6 The interval over which the function is strictly decreasing: [4,infinity) (-infinity,-4] 34. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/sw4 2 7.pg Consider the function given in the following graph. What is its domain?

7 What is its range? Note: Write the answer in interval notation. [-3,3] [-1,2] 35. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/jj1.pg Consider the function shown in the following graph x + y = x = y (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/4.pg Enter Yes or No in each answer space below to indicate whether the corresponding equation defines y as a function of x. Note: Be careful, You only have TWO chances to get them right x + y = x = y 2 3. x + 6 = y 2 4. x 2 + 2y = 7 Where is the function decreasing? Note: use interval notation to enter your answer. (-3,5) 39. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs- /ns pg 36. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/5.pg Enter Yes or No in each answer space below to indicate whether the corresponding equation defines y as a function of x. Note: Be careful, You only have TWO chances to get them right x + y = x = y 3 3. x + 10 = y x = y (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/6.pg Enter Yes or No in each answer space below to indicate whether the corresponding equation defines y as a function of x. Note: Be careful, You only have TWO chances to get them right. 1. x 2 + 5y = 6 2. x + 3 = y 2 7 Write the equation describing the graph above: 0*(x + 5) *(x - 2) for x in the interval [ to ] for x in the interval [ to ]

8 40. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs- /sw pg Enter Yes or No in each answer space below to indicate whether the corresponding equation defines y as a function of x. Note: Be careful, You only have TWO chances to get them right. 42. (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/sw4 2 1.pg For the function h(x) given in the graph 1. x + 1 = y 2 2. x 2 + 5y = x = y x = y (1 pt) Library/Rochester/setAlgebra16FunctionGraphs/ns1 1 2.pg its domain is ; its range is ; Write the answer in interval notation. and then enter the corresponding function value in each answer space below: Given the graphs of f (in blue) and g (in red) to the left answer these questions: 1. What is the value of f at -5? 2. For what values of x is g(x): Separate answers by spaces (e.g 5 7 ) 3. Estimate the solution of the equation g(x) = 5 4. On what interval is the function f decreasing? (Separate answers by a space: e.g ) h(1) 2. h( 2) 3. h( 1) 4. h(0) [-3,3] [-2,2] (1 pt) Library/Rochester/setAlgebra16FunctionGraphs- /c2s2p59 72/c2s2p59 72.pg Match the functions with their graphs. Enter the letter of the graph below which corresponds to the function. (Click on image for a larger view ) 1. Piecewisefucntion : 1, ifx < 2and 1, ifx 2 2. Piecewisefucntion : 2, ifx 1and x 2, ifx > 1 3. Piecewisefucntion : x, ifx 0and x + 1, ifx > 0 4. Piecewisefucntion : 1 x, ifx < 2and 4, ifx 2 A B C D

9 D B A C 44. (1 pt) Library/Rochester/setAlgebra17FunComposition- /srw mo.pg Express the function h(x) = (x + 3) 6 in the form f g. If x 6, find the function g(x). Your answer is g(x)=, x (1 pt) Library/Rochester/setAlgebra17FunComposition- /s0 1 84a.pg Let 2x + 4 and g(x) = 5x 2 + 3x. After simplifying, ( f g)(x) = 10*xˆ3+26*xˆ2+12*x 1. g(x) f (x) 2. (g(x)) 2 3. ( f (x)) 2 4. g( f (x)) A. 2 + x 3 B x 3 + x 6 C x + x 2 D. 1 + x + x 3 + x 4 D C B A 49. (1 pt) Library/Rochester/setAlgebra17FunComposition- /sw pg Click on the graph to view a larger graph For the function f (x) and g(x) are given in the following graph. 46. (1 pt) Library/Rochester/setAlgebra17FunComposition/pcomp.pg Given that x 2 4x and g(x) = x 9, calculate (a) f g(x)=, (b) g f (x)=, (c) f f (x)=, (d) g g(x)=, (x+-9)**2+-4*(x+-9) x**2+-4*x+-9 (x**2+-4*x)**2+-4*(x**2+-4*x) x+2*-9 Find the corresponding function values. 47. (1 pt) Library/Rochester/setAlgebra17FunComposition- /ur fn 2 10.pg Let 1 x 7 and g(x) = 7 x + 7. Then ( f g)(x) =, (g f )(x) =. x/7 7*x-7* (1 pt) Library/Rochester/setAlgebra17FunComposition/c0s1p9.pg This problem gives you some practice identifying how more complicated functions can be built from simpler functions. Let x 3 + 1and let g(x) = x + 1. Match the functions defined below with the letters labeling their equivalent expressions f (g(0)) 2. f (g(2)) (1 pt) Library/Rochester/setAlgebra17FunComposition/s pg Let 2x + 4 and g(x) = 5x 2 + 3x. ( f + g)(4) = 104

10 51. (1 pt) Library/Rochester/setAlgebra17FunComposition- /ur fn 2 5.pg Let 1 1 and g(x) = x 3 x 1. Then the domain of f g is equal to all reals except for two values, a and b with a < b and a = b = (1 pt) Library/Rochester/setAlgebra17FunComposition- /ur fn 2 2.pg This problem tests calculating new functions from old ones. From the table below calculate the quantities asked for: x f (x) g(x) ( f g)( 2) = ( f + g)(3) = g( f (3)) = (1 pt) Library/Rochester/setAlgebra24Variation/lh pg A company has found that the demand for its product varies inversely as the price of the product. When the price x is 4.75 dollars, the demand y is 550 units. Find a mathematical model that gives the demand y in terms of the price x in dollars. Your answer is y = Approximate the demand when the price is 9 dollars. Your answer is: 4.75*550/x (1 pt) Library/Rochester/setAlgebra24Variation/joint.pg Suppose p varies jointly as the square of q and the cube root of r. If p = 8 when q = 3 and r = 4, what is p if q = 15 and r = 6? p = (1 pt) Library/Rochester/setAlgebra15Functions/s0 1 2a.pg Let 3x 2 f (1 + h) f (1) + 5x + 3 and let q(h) =. Then h q(0.01) = (1 pt) Library/Rochester/setAlgebra15Functions/lh pg Given the function { 2x if x < 1 4x if x 1 Calculate the following values: f ( 2) = f (1) = f (2) = (1 pt) Library/Rochester/setAlgebra15Functions/srw pg Given the function 4 x 8, calculate the following values: f (0) = f (2) = f ( 2) = f (x + 1) = f (x 2 + 2) = Note: In your answer, you may use abs(g(x)) for g(x) *abs(x+1-8) 4*abs(x**2+2-8) 58. (1 pt) Library/Rochester/setAlgebra15Functions/jay4.pg An open box is to be made from a flat square piece of material 16 inches in length and width by cutting equal squares of length x from the corners and folding up the sides. Write the volume V of the box as a function of x. Leave it as a product of factors; you do not have to multiply out the factors. V = If we write the domain of the box as an open interval in the form (a,b), then what is a? a = and what is b? b = ((16-2x)(16-2x)x)

11 59. (1 pt) Library/Rochester/setAlgebra15Functions/p2.pg The domain of the function 4x x 2 1 is Write the answer in interval notation. Note: If the answer includes more than one interval write the intervals separated by the union symbol, U. If needed enter as - infinity and as infinity. (-1,0] U (1,infinity) 60. (1 pt) Library/Rochester/setAlgebra15Functions/p4.pg Find domain and range of the function 15x 2 2 E E 63. (1 pt) Library/Rochester/setAlgebra15Functions/srw pg Given the function 3 + 5x 2, calculate the following values: f (a) = f (a + h) = f (a + h) f (a) = h 5*a**2+3 5*(a+h)**2+3 5*2*a+5*h 64. (1 pt) Library/Rochester/setAlgebra15Functions/p1.pg The domain of the function 1 18x + 18 Domain: Range: Write the answer in interval notation. Note: If the answer includes more than one interval write the intervals separated by the union symbol, U. If needed enter as - infinity and as infinity. (-infinity,infinity) [-2,infinity) 61. (1 pt) Library/Rochester/setAlgebra15Functions/srw pg The domain of the function 8x + 14, 8 x 3 is. Write the answer in interval notation. Note: If the answer includes more than one interval write the intervals separated by the union symbol, U. If needed enter as - infinity and as infinity. [-8,3] 62. (1 pt) Library/Rochester/setAlgebra15Functions/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! 1. x 2 + 3x 4 + 2x 3 2. x 3 + x 5 + x 3 3. x 2 6x 4 + 3x 2 4. x 6 N O 11 is Write the answer in interval notation. Note: If the answer includes more than one interval write the intervals separated by the union symbol, U. If needed enter as - infinity and as infinity. (-1,infinity) 65. (1 pt) Library/Rochester/setAlgebra15Functions/sw pg Let 2. Calculate the following values: f (a) = f (a + h) = f (a + h) f (a) = for h 0 h (1 pt) Library/Rochester/setAlgebra15Functions/box.pg An open box is to be made from a flat piece of material 13 inches long and 5 inches wide by cutting equal squares of length x from the corners and folding up the sides. Write the volume V of the box as a function of x. Leave it as a product of factors, do not multiply out the factors. V (x) = If we write the domain of V (x) as an open interval in the form (a,b), then what is a? a = and what is b? b = ((13-2x)(5-2x)x) 0.5

12 67. (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH Linear-expressions.pg Is the expression 3xy + 2x y linear in the variable y? If it is linear, enter the slope. If it is not linear, enter NO. 3 * x (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH b-Linear-expressions.pg Linear Linear Linear Linear Linear t Linear t Linear 70. (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH Linear-expressions.pg Is the expression ax 2 + 2x + 4 linear in the variable x? If it is linear, enter the slope. If it is not linear, enter NO. Find an equation for of each of the lines in the figure. Line A (in red) has equation y = Line B (in blue) has equation y = NO 71. (1 pt) Library/FortLewis/Algebra/5-4-Equations-for-lines/MCH Equations-for-lines.pg Write the equation for the line 2x + 5y = 8 in the form y = mx + b, and enter it in this form. y = (-2/5) x + 8/5 72. (1 pt) Library/FortLewis/Algebra/9-3-Completing-the-square- /MCH Completing-the-square.pg Solve the quadratic equation x 2 8x 3 = 0. If there is more than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE. x = , *x+6 1.5*x+1 (Click on graph to enlarge) 73. (1 pt) Library/FortLewis/Algebra/9-3-Completing-the-square- /MCH Completing-the-square.pg (a) Complete the square by writing 3x x + 1 in the form a(x h) 2 + k. Note: the numbers a,h and k can be positive or negative. 69. (1 pt) Library/FortLewis/Algebra/5-2-Linear-expressions/MCH Linear-expressions.pg Are the expressions linear or not?? 1. 5r 2 + 2? 2. (3a + 1)/4? 3. 5t 8? 4. 6r + r 1? (1/3)x? 6. 6A 3(1 3A)? 7. (3a + 1)/a? 8. 5 x + 1 t Linear 12 3x x + 1 = ( ) 2 + (b) Solve the equation 3x x + 1 = 0 by completing the square or using the quadratic formula. If there is more than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE. x = 3 x ,

13 74. (1 pt) Library/FortLewis/Algebra/9-3-Completing-the-square- /MCH Completing-the-square.pg (a) Complete the square by writing 2x 2 + 2x + 3 in the form a(x h) 2 + k. Note: the numbers a,h and k can be positive or negative. 2x 2 + 2x + 3 = ( ) 2 + (b) Solve the equation 2x 2 + 2x + 3 = 0 by completing the square or using the quadratic formula. If there is more than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE. x = x+1/2.5 NONE 75. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg Write the expression x x + 30 in factored form k(ax + b)(cx + d). x x + 30 = (x+5)(x+6) 76. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg The quadratic expression (x 3) 2 36 is written in vertex form. (a) Write the expression in standard form ax 2 + bx + c. (b) Write the expression in factored form k(ax + b)(cx + d). (c) Evaluate the expression at x = 0 using each of the three forms, compare the results, and enter your answer below. 77. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg Put the function y = 5x x + 17 in vertex form a(x h) 2 + k and determine the values of a,h, and k. a = h = k = (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg Suppose y = 2x x 74. In each part below, if there is more than one correct answer, enter your answers as a comma separated list. If there are no correct answers, enter NONE. (a) Find the y-intercept(s). y = (b) Find the x-intercept(s). x = , (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg Find the minimum and maximum value of the function y = (x 2) Enter infinity or -infinity if the function never stops increasing or decreasing. Maximum value = Minimum value = inf 9 (d) Evaluate the expression at x = 5 using each of the three forms, compare the results, and enter your answer below. xˆ2-6*x-27 (x+3) (x-9) (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg The height of a right triangle is 7 feet more than three times the length of its base. Express the area of the triangle as a function of the length of its base, x, in feet. x*(3*x+7)/2 square feet

14 81. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg Find a possible formula for the quadratic function in the graph. 85. (1 pt) Library/Rochester/setLimitsRates2Limits/s mo.pg Evaluate the it ((1)ˆ2+1 +1)/(1+1) s 3 1 s 1 s (1 pt) Library/Rochester/setLimitsRates2Limits/s mo.pg Evaluate the it 16 s 4 s s 16 -(x+2)*(x-3) 82. (1 pt) Library/FortLewis/Algebra/9-2-Quadratic-expressions- /MCH Quadratic-expressions.pg Find the vertex of the parabola y = 6x + 7 x 2. Enter your answer as a point (h,k), including the parentheses. The vertex is at the point (3,16) 83. (1 pt) Library/Rochester/setLimitsRates2Limits/s pg Evaluate the it 49 b b 49 7 b (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 7.pg Let x2 11x+28 x 2 +3x 28. Calculate x 4 f (x) by first finding a continuous function which is equal to f everywhere except x = 4. x (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 48a.pg Evaluate the its. If a it does not exist, enter DNE. x + 6 x 6 + x + 6 = x + 6 x 6 x + 6 = x + 6 x 6 x + 6 = 1-1 DNE 88. (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 13.pg The main theorem of Ste 2.3 tells us that many functions are continuous so that their its can be evaluated by direct substitution. Calculate the following its by direct substitution, making use of this big theorem from Ste 2.3. x 3 2x3 4x 10 = (6 y 1 y)(y2 + 1) 3 = a 10 (a + 7) 4 a + 1 = 3(x ) = x 0 s 8 y 2 y3 (5 3y 2 ) = 13 s s + 12 = 14

15 89. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 4.pg Evaluate the it 4(3x + 4)3 x (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 5.pg 1 x + 3, if x < 2 Let 3, if x = 2 2x + 8, if x > 2 Calculate the following its. Enter DNE for a it which does not exist. x 2 x 2 + x (1 pt) Library/Rochester/setLimitsRates2Limits/s pg Evaluate the it 5(y 2 1) y 4 7y 2 (y 1) 3 Note: you can click on the graph to get a larger image. Determine the its for the function f at x = 1. Note: its are all integers (e.g., 2, 1,0,1,2, ). x 1 f (1) = x 1 + Is this function continuous at x = 1?: Can one change the value of this function at x = 1 to some value other than its current value at x = 1, and have the function be continuous at x = 1?: -3-1 no 93. (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 5 mo.pg Evaluate the it x 5 x 3 6x 2 4x (1 pt) Library/Rochester/setLimitsRates2Limits/ns2 2 6.pg Let f be the function below (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 4.pg { 6 x x 2, if x 2 Let 2x 5, if x > 2 Calculate the following its. Enter 1000 if the it does not exist. x 2 x 2 + x (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 3 mo.pg Evaluate the it ( 7x ) (5x + 8) x

16 96. (1 pt) Library/Rochester/setLimitsRates2Limits/s pg Evaluate the it x + 15 x 15 x (1 pt) Library/Rochester/setLimitsRates2Limits/s pg Evaluate the it -1 x x + 42 x 7 x (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 10b.pg a f (x) x a DNE f (x) DNE x a + f (a) g(x) DNE x a g(x) DNE x a + g(a) Using the table above calcuate the its below. Enter DNE if the it doesn t exist OR if it can t be determined from the information given. 1. f (1)g(1) 2. f (g(x))] x 1 [ 3. f (x)/g(x)] x 1 [ 4. f (1)/g(1) 6 3 DNE (1 pt) Library/Rochester/setLimitsRates2Limits/s pg Evaluate the it x 3 x 3 x 2 + 6x (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 8.pg Let 4x+8 x 2 5x 14. Calculate f (x) by first finding a continuous function which x 2 is equal to f everywhere except x = 2. x (1 pt) Library/Rochester/setLimitsRates2Limits/s pg Evaluate the it 1 t 3 t t 1 t (1 pt) Library/Rochester/setLimitsRates2Limits/s1 3 5.pg Evaluate the it If x x 6 6x 2 6x (1 pt) Library/Rochester/setLimitsRates2Limits/ur lr 2 11.pg 9x 29 f (x) x 2 + 3x 20 determine x 3 What theorem did you use to arrive at your answer? -2 The Squeeze theorem 104. (1 pt) Library/Rochester/setLimitsRates2Limits/s pg The slope of the tangent line to the graph of the function y = 3x 3 3x at the point (2,24) is 3 24 x 2 x 2. By trying values of x near 2, find the slope of the tangent line

17 105. (1 pt) Library/Rochester/setLimitsRates6Rates/s1 6 3.pg The slope of the tangent line to the curve y = 2 x at the point (6,4.8990) is: The equation of this tangent line can be written in the form y = mx + b where m is: and where b is: (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 8.pg Find c such that the function { x 2 4, x c 8x 20, x > c is continuous everywhere. c = (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 1.pg A function f (x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or not continuous at x = a. 2. f (a) could either be defined or redefined so that the new function IS continuous at x = a. Let 2x2 +3x 44 x 4 Show that f (x) has a removable discontinuity at x = 4 and determine what value for f (4) would make f (x) continuous at x = 4. Must define f (4) = (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 4.pg A function f (x) is said to have a jump discontinuity at x = a if: 1. f (x) exists. x a 2. f (x) exists. x a + 3. The left and right its are not equal (1 pt) Library/Rochester/setLimitsRates5Continuity/ur lr 5 5.pg A function f (x) is said to have a jump discontinuity at x = a if: 1. f (x) exists. x a 2. f (x) exists. x a + 3. The left and right its are not equal. x 2 + 5x + 6, if x < 8 Let 25, if x = 8 3x + 2, if x > 8 Show that f (x) has a jump discontinuity at x = 8 by calculating the its from the left and right at x = 8. x 8 x 8 + Now for fun, try to graph f (x) (1 pt) Library/Rochester/setLimitsRates5Continuity/s pg For what value of the constant c is the function f continuous on (, ) where { ct + 2 if t (,2] f (t) = ct 2 2 if t (2, ) 111. (1 pt) Library/Michigan/Chap1Sec7/Q17.pg Find k so that the following function is continuous on any interval: kx if 0 x < 1, and 7x 2 if 1 x. k = 7*1 { 4x 1, if x < 7 Let 2 x+5, if x 7 Show that f (x) has a jump discontinuity at x = 7 by calculating the its from the left and right at x = 7. x 7 x 7 + Now for fun, try to graph f (x) (1 pt) Library/Michigan/Chap1Sec7/Q19.pg If possible, choose k so that the following function is continuous on any interval: { 6x 5 12x 4 x 2 x 2 k x = 2. k = (If no k will make the function continuous, enter none)

18 6*(2)ˆ (1 pt) Library/Michigan/Chap1Sec8/Q21.pg For the function x 2 4, 0 x < 3 0, x = 3 2x 1, 3 < x use algebra to find each of the following its: x 3 + x 3 x 3 (For each, enter dne if the it does not exist.) Sketch a graph of f (x) to confirm your answers. * *3-4 3* (1 pt) Library/Union/setLimitConcepts/ur lr pg Let F be the function whose graph is shown below. Evaluate each of the following expressions. (If a it does not exist or is undefined, enter DNE.) 1. x 1 = 2. x 1 + = 3. x 1 = 4. F( 1) = 5. x 1 6. x F(x) = x 1 8. F(x) x 3 = 9. F(3) = 114. (1 pt) Library/Union/setLimitInfinity/ns2 2 xxx.pg Evaluate the following its: 2 1. x 5 (x 5) 3 = 2. 1 x 0 x 2 (x + 7) 3. 2 x 3 + x x 7 x 2 (x + 7) -infinity infinity infinity -infinity = = = DNE 1 DNE The graph of y = F(x). Generated by c WeBWorK, Mathematical Association of America 18