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Discuss any limitations that exist for this solution
One limitation based on the scenarios is about the wearing down rate which is thought to be
toward the end of the month. Attrition rate is likewise normally alluded ...
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MA302 Grantham Week 3 Calculus Functions and Graphs Practice Paper
Assignment SubmissionFor this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.Assignment ScoringYour last submission is used for your score.Consider the following function and graph.f(x) = 3xx2 − 9Determine whether f(x) approaches ∞ or -∞ as x approaches 3 from the left and from the right.(a)lim x→3− f(x) (b)lim x→3+ f(x) 2.–/11 pointsLarCalc11 1.5.011.Ask Your TeacherMy NotesConsider the following function.f(x) = 1x2 − 16Complete the following table. (Round your answers to two decimal places.)x−4.5−4.1−4.01−4.001−4−3.999−3.99−3.9−3.5f(x)?Use the table to determine whether f(x) approaches ∞ or −∞ as x approaches −4 from the left and from the right. lim x→−4− f(x) = lim x→−4+ f(x) = Use a graphing utility to graph the function to confirm your answer. 3.–/1 pointsLarCalc11 1.5.040.Ask Your TeacherMy NotesFind the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (−1/2)+ 6x2 + x − 110x2 − 5x − 5 4.–/1 pointsLarCalc11 1.5.041.Ask Your TeacherMy NotesFind the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)lim x→0− 6 + 5x 5.–/1 pointsLarCalc11 1.5.046.Ask Your TeacherMy NotesFind the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (π/2)+ −8cos x 6.–/1 pointsLarCalc11 2.1.010.Ask Your TeacherMy NotesFind the slope of the tangent line to the graph of the function at the given point. g(x) =7x + 7, (-6, 0)6 7.–/1 pointsLarCalc11 2.1.021.Ask Your TeacherMy NotesFind the derivative of the function by the limit process.f(x) = x2 + x − 5f '(x) = 8.–/1 pointsLarCalc11 2.1.025.Ask Your TeacherMy NotesFind the derivative of the function by the limit process.f(x) = 7x − 8f '(x) = 9.–/1 pointsLarCalc11 2.1.038.Ask Your TeacherMy NotesFind an equation of the line that is tangent to the graph of f and parallel to the given line.FunctionLinef(x) = 2x24x − y + 1 = 0y = 10.–/1 pointsLarCalc11 2.2.013.Ask Your TeacherMy NotesUse the rules of differentiation to find the derivative of the function.f(x) = 4xf '(x) = 11.–/1 pointsLarCalc11 2.2.017.Ask Your TeacherMy NotesUse the rules of differentiation to find the derivative of the function.f(t) = 5t2 + 4t + 1f '(t) = 12.–/1 pointsLarCalc11 2.2.026.Ask Your TeacherMy NotesUse the rules of differentiation to find the derivative of the function.y = 3x4 + 8 sin xy' = 13.–/4 pointsLarCalc11 2.2.027.Ask Your TeacherMy NotesComplete the table to find the derivative of the function.Original FunctionRewriteDifferentiateSimplifyy = 35x4 x 14.–/1 pointsLarCalc11 2.2.035.Ask Your TeacherMy NotesFind the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.FunctionPointy = (8x + 2)2, (0, 4)y'(0) = 15.–/1 pointsLarCalc11 2.2.041.Ask Your TeacherMy NotesFind the derivative of the function.g(t) = t2 − 4t3g'(t) = 16.–/1 pointsLarCalc11 2.2.043.Ask Your TeacherMy NotesFind the derivative of the function.f(x) = x3 − 3x2 + 9x2f '(x) = 17.–/1 pointsLarCalc11 2.2.049.Ask Your TeacherMy NotesFind the derivative of the function.f '(x) = 18.–/2 pointsLarCalc11 2.2.055.Ask Your TeacherMy NotesConsider the given function and point.f(x) = −8x4 + 11x2 − 3,(1, 0)(a)Find an equation of the tangent line to the graph of the function at the given point.y = (b)Use a graphing utility to graph the function and its tangent line at the point. Use the tangent feature of the graphing utility to confirm your results. 19.–/7 pointsLarCalc11 2.2.095.Ask Your TeacherMy NotesA silver dollar is dropped from the top of a building that is 1398 feet tall. Use the position function below for free-falling objects.s(t) = −16t2 + v0t + s0(a) Determine the position and velocity functions for the coin.s(t) = v(t) = (b) Determine the average velocity on the interval [1, 2]. ft/s(c) Find the instantaneous velocities when t = 1 second and t = 2 seconds.v(1) = ft/sv(2) = ft/s(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.)t = s(e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/s 20.–/1 pointsLarCalc11 2.3.009.MI.Ask Your TeacherMy NotesUse the Product Rule to differentiate the function.f(x) = x3 cos(x)f '(x) = 21.–/1 pointsLarCalc11 2.3.011.Ask Your TeacherMy NotesUse the Quotient Rule to find the derivative of the function.f(x) = xx − 4 f '(x) = 22.–/2 pointsLarCalc11 2.3.017.Ask Your TeacherMy NotesFind f '(x) and f '(c).FunctionValue of cf(x) = (x3 + 2x)(3x4 + 3x − 2) c = 0f '(x) = f '(c) = 23.–/2 pointsLarCalc11 2.3.022.Ask Your TeacherMy NotesFind f '(x) and f '(c).FunctionValue of cf(x) = sin xxc = π6f '(x)= f '(c)= 24.–/4 pointsLarCalc11 2.3.025.MI.SA.Ask Your TeacherMy NotesThis question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. 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URGENT: mystatlab homework
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5 pages
Answer 1
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MA302 Grantham Week 3 Calculus Functions and Graphs Practice Paper
Assignment SubmissionFor this assignment, you submit answers by question parts. The number of submissions remaining for ea ...
MA302 Grantham Week 3 Calculus Functions and Graphs Practice Paper
Assignment SubmissionFor this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.Assignment ScoringYour last submission is used for your score.Consider the following function and graph.f(x) = 3xx2 − 9Determine whether f(x) approaches ∞ or -∞ as x approaches 3 from the left and from the right.(a)lim x→3− f(x) (b)lim x→3+ f(x) 2.–/11 pointsLarCalc11 1.5.011.Ask Your TeacherMy NotesConsider the following function.f(x) = 1x2 − 16Complete the following table. (Round your answers to two decimal places.)x−4.5−4.1−4.01−4.001−4−3.999−3.99−3.9−3.5f(x)?Use the table to determine whether f(x) approaches ∞ or −∞ as x approaches −4 from the left and from the right. lim x→−4− f(x) = lim x→−4+ f(x) = Use a graphing utility to graph the function to confirm your answer. 3.–/1 pointsLarCalc11 1.5.040.Ask Your TeacherMy NotesFind the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (−1/2)+ 6x2 + x − 110x2 − 5x − 5 4.–/1 pointsLarCalc11 1.5.041.Ask Your TeacherMy NotesFind the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)lim x→0− 6 + 5x 5.–/1 pointsLarCalc11 1.5.046.Ask Your TeacherMy NotesFind the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) lim x → (π/2)+ −8cos x 6.–/1 pointsLarCalc11 2.1.010.Ask Your TeacherMy NotesFind the slope of the tangent line to the graph of the function at the given point. g(x) =7x + 7, (-6, 0)6 7.–/1 pointsLarCalc11 2.1.021.Ask Your TeacherMy NotesFind the derivative of the function by the limit process.f(x) = x2 + x − 5f '(x) = 8.–/1 pointsLarCalc11 2.1.025.Ask Your TeacherMy NotesFind the derivative of the function by the limit process.f(x) = 7x − 8f '(x) = 9.–/1 pointsLarCalc11 2.1.038.Ask Your TeacherMy NotesFind an equation of the line that is tangent to the graph of f and parallel to the given line.FunctionLinef(x) = 2x24x − y + 1 = 0y = 10.–/1 pointsLarCalc11 2.2.013.Ask Your TeacherMy NotesUse the rules of differentiation to find the derivative of the function.f(x) = 4xf '(x) = 11.–/1 pointsLarCalc11 2.2.017.Ask Your TeacherMy NotesUse the rules of differentiation to find the derivative of the function.f(t) = 5t2 + 4t + 1f '(t) = 12.–/1 pointsLarCalc11 2.2.026.Ask Your TeacherMy NotesUse the rules of differentiation to find the derivative of the function.y = 3x4 + 8 sin xy' = 13.–/4 pointsLarCalc11 2.2.027.Ask Your TeacherMy NotesComplete the table to find the derivative of the function.Original FunctionRewriteDifferentiateSimplifyy = 35x4 x 14.–/1 pointsLarCalc11 2.2.035.Ask Your TeacherMy NotesFind the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.FunctionPointy = (8x + 2)2, (0, 4)y'(0) = 15.–/1 pointsLarCalc11 2.2.041.Ask Your TeacherMy NotesFind the derivative of the function.g(t) = t2 − 4t3g'(t) = 16.–/1 pointsLarCalc11 2.2.043.Ask Your TeacherMy NotesFind the derivative of the function.f(x) = x3 − 3x2 + 9x2f '(x) = 17.–/1 pointsLarCalc11 2.2.049.Ask Your TeacherMy NotesFind the derivative of the function.f '(x) = 18.–/2 pointsLarCalc11 2.2.055.Ask Your TeacherMy NotesConsider the given function and point.f(x) = −8x4 + 11x2 − 3,(1, 0)(a)Find an equation of the tangent line to the graph of the function at the given point.y = (b)Use a graphing utility to graph the function and its tangent line at the point. Use the tangent feature of the graphing utility to confirm your results. 19.–/7 pointsLarCalc11 2.2.095.Ask Your TeacherMy NotesA silver dollar is dropped from the top of a building that is 1398 feet tall. Use the position function below for free-falling objects.s(t) = −16t2 + v0t + s0(a) Determine the position and velocity functions for the coin.s(t) = v(t) = (b) Determine the average velocity on the interval [1, 2]. ft/s(c) Find the instantaneous velocities when t = 1 second and t = 2 seconds.v(1) = ft/sv(2) = ft/s(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.)t = s(e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/s 20.–/1 pointsLarCalc11 2.3.009.MI.Ask Your TeacherMy NotesUse the Product Rule to differentiate the function.f(x) = x3 cos(x)f '(x) = 21.–/1 pointsLarCalc11 2.3.011.Ask Your TeacherMy NotesUse the Quotient Rule to find the derivative of the function.f(x) = xx − 4 f '(x) = 22.–/2 pointsLarCalc11 2.3.017.Ask Your TeacherMy NotesFind f '(x) and f '(c).FunctionValue of cf(x) = (x3 + 2x)(3x4 + 3x − 2) c = 0f '(x) = f '(c) = 23.–/2 pointsLarCalc11 2.3.022.Ask Your TeacherMy NotesFind f '(x) and f '(c).FunctionValue of cf(x) = sin xxc = π6f '(x)= f '(c)= 24.–/4 pointsLarCalc11 2.3.025.MI.SA.Ask Your TeacherMy NotesThis question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial ExerciseFind the derivative of the function without using the Quotient Rule. 1513x4 25.–/1 pointsLarCalc11 2.3.029.Ask Your TeacherMy NotesFind the derivative of the function.f(x) = 4 − 5x − x2x2 − 6 f '(x) = 26.–/1 pointsLarCalc11 2.3.033.Ask Your TeacherMy NotesFind the derivative of the function.f(x) = 9x − 1xf '(x) = 27.–/1 pointsLarCalc11 2.3.041.Ask Your TeacherMy NotesQuestion PartPointsSubmissions UsedFind the derivative of the trigonometric function.f(t) = t9 sin(t)f '(t) = 28.–/1 pointsLarCalc11 2.3.043.Ask Your TeacherMy NotesQuestion PartPointsSubmissions UsedFind the derivative of the trigonometric function.f(t) = cos(t)tf '(t) = 29.–/1 pointsLarCalc11 2.3.049.Ask Your TeacherMy NotesQuestion PartPointsSubmissions UsedFind the derivative of the trigonometric function.y = 5(1 − sin(x))2 cos(x)y' =
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