Calculus Answers, Learning Aids & Study Resources

11. Evaluate the limit using L'Hopital's Rule if necessary. a.

11. Evaluate the limit using L'Hopital's Rule if necessary. a. -? b. ? c. 2/7 d. 0 e. 7/2 12. Evaluate the limit using L'Hopital's Rule if necessary. a. 1/3 b. 1/24 c. -? d. ? e. 2 13. Evaluate the limit using L'Hopital's Rule if necessary. a. 8/7 b. 56 c. ? d. 0 e. does not exist 14. Evaluate the limit using.

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11. Evaluate the limit using L'Hopital's Rule if necessary. a.

Calculus

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9.8 Power Series Multiple Choice Identify the choice that best

9.8 Power Series Multiple Choice Identify the choice that best completes the statement or answers the question. 1. State where the power series is centered. a. 0 b. –3 c. 2 d. 3 e. –2 2. Find the radius of convergence of the power series. a. 1/25 b. 1/5 c.5 d. ? e. 25 3. Find the radius of.

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9.8 Power Series Multiple Choice Identify the choice that best

Calculus

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____ 6. Use the Direct Comparison Test to determine the

6. Use the Direct Comparison Test to determine the convergence or divergence of the Series a. The series converges. b. The series diverges. 7. Use the Direct Comparison Test to determine the convergence or divergence of the series . a. The series diverges. b. The series converges. 8. Use the.

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____ 6. Use the Direct Comparison Test to determine the

Calculus

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Multiple Choice Identify the choice that best completes the statement

Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the first five terms of the sequence. a. b. c. d. e. 2. Write the first five terms of the sequence. a. b. c. d. e. 3. Write the first three terms of.

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Multiple Choice Identify the choice that best completes the statement

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9.2 Series and Convergence Multiple Choice Identify the choice that

9.2 Series and Convergence Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. Write the first five terms of the sequence of partial sums. a. b. c. d. e. __ 2. Write the first five terms of the sequence of partial sums. a. b. c. d..

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9.2 Series and Convergence Multiple Choice Identify the choice that

Calculus

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____ 6. Find the interval of convergence of the power

6. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) a. b. c. d. e. 7. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the.

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____ 6. Find the interval of convergence of the power

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____ 15. Find the positive values of for which the

15. Find the positive values of for which the series converges. a. The series converges for p > 4. b. The series converges for p > 11. c. The series diverges for all positive values of p. d. The series converges for p > 1. e. The series converges for p ? 8. .

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____ 15. Find the positive values of for which the

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6. Use integration tables to find a. b. c. d.

6. Use integration tables to find a. b. c. d. e. 7. Use integration tables to evaluate the integral a. b. c. d. e. 8. Use integration tables to evaluate the integral a. 21 ? b. c. d. e. 9. Use integration tables to evaluate the integral a. b. c. d..

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6. Use integration tables to find a. b. c. d.

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____ 11. True or false. The series convergent. a. false b.

11. True or false. The series is convergent. a. false b. true 12. True or false. The series is divergent. a. false b. true 13. Determine the convergence or divergence of the series. a. cannot be determined from the methods in the chapter b. Diverges c. Converges 14. Find all values of x.

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____ 11. True or false. The series convergent. a. false b.

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9.6 The Ratio and Root Test Multiple Choice Identify the choice that

9.6 The Ratio and Root Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use the Ratio Test to determine the convergence or divergence of the series . a. converges b. diverges 2. Use the Ratio Test to determine the convergence or divergence of the series. a. diverges b..

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9.6 The Ratio and Root Test Multiple Choice Identify the choice that

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8.8 Improper Integrals Multiple Choice 1. Determine whether the improper integral

8.8 Improper Integrals Multiple Choice 1. Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. a. 100 b. 2 c. 1/50 d. 22/9 e. diverges 2. Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. a. 1/2 b. 1/6 c. 2 d. 1/32 e. diverges 3. Determine whether the improper integral diverges.

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8.8 Improper Integrals Multiple Choice 1. Determine whether the improper integral

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8.7 Indeterminate Forms and L’Hôpital’s Rule Multiple Choice 1. Evaluate the limit

8.7 Indeterminate Forms and L’Hôpital’s Rule Multiple Choice 1. Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule. a. 9/20 b. – 9/100 c. - 9/20 d. 0 e. does not exist 2. Evaluate the limit first by using techniques from Chapter 1 then by using L'Hopital's Rule. a. 8 b. 0 c..

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8.7 Indeterminate Forms and L’Hôpital’s Rule Multiple Choice 1. Evaluate the limit

Calculus

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____ 6. Find the sum of the convergent series. a. b.

6. Find the sum of the convergent series. a. b. c. d. e. 7. Find the sum of the convergent series. a. b. c. d. e. 8. Find the sum of the convergent series a. b. c. d. e. 9. Find the sum of the convergent series a..

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____ 6. Find the sum of the convergent series. a. b.

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11. Determine whether the improper integral diverges or converges. Evaluate

11. Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. a. b. c. diverges d. e. 12. Find the area between the x-axis and the graph of the function a. 2? b. 2 c. 3 d. 3? e. 0 13. Suppose the capitalized cost C is given by where C0 is.

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11. Determine whether the improper integral diverges or converges. Evaluate

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9.3 The Integral Test and p-Series Multiple Choice Identify the

9.3 The Integral Test and p-Series Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use the Integral Test to determine the convergence or divergence of the series. a. diverges b. Integral Test inconclusive c. converges 2. Use the Integral Test to determine the convergence or divergence.

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9.3 The Integral Test and p-Series Multiple Choice Identify the

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8.3 Trigonometric Integrals Multiple Choice 1. Find the indefinite integral. a. b. c.

8.3 Trigonometric Integrals Multiple Choice 1. Find the indefinite integral. a. b. c. d. e. 2. Find the indefinite integral. a. b. c. d. e. 3. Find the indefinite integral. a. b. c. d. e. 4. Find the indefinite integral. a. b. c. d. e. 5. Find the indefinite integral. a. b. c. d. e. .

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8.3 Trigonometric Integrals Multiple Choice 1. Find the indefinite integral. a. b. c.

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6. Find the indefinite integral a. b. c. d. e.

6. Find the indefinite integral a. b. c. d. e. 7. Find the indefinite integral a. b. c. d. e. 8. Find the indefinite integral. a. b. c. d. e. 9. Find the indefinite integral a. b. c. d. e. 10. Solve the differential equation a. b. c. d. e. .

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6. Find the indefinite integral a. b. c. d. e.

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____ 6. Use the Root Test to determine the convergence

6. Use the Root Test to determine the convergence or divergence of the series . a. converges b. diverges 7. Use the Root Test to determine the convergence or divergence of the series. a. converges b. diverges c. Root Test inconclusive 8. Use the Root Test to determine the convergence or divergence of the.

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____ 6. Use the Root Test to determine the convergence

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6. Evaluate the limit using L'Hopital's Rule if necessary. a.

6. Evaluate the limit using L'Hopital's Rule if necessary. a. 2/13 b. 0 c. 1/2 d. 13/2 e. does not exist 7. Evaluate the using L’Hôpital’s Rule if necessary. a. 1/2 b. - 8/9 c. 5/9 d. 0 e. ? 8. Evaluate the using L’Hôpital’s Rule if necessary. a. 1/6 b. 1/4 c. 1/2 d. ? e. 0 9. Evaluate the limit using L'Hopital's.

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6. Evaluate the limit using L'Hopital's Rule if necessary. a.

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____ 11. Use the Limit Comparison Test (if possible) to

11. Use the Limit Comparison Test (if possible) to determine whether the series converges or diverges. a. diverges b. converges 12. Use the Limit Comparison Test (if possible) to determine whether the series converges or diverges. a. converges b. diverges 13. Use the Limit Comparison Test to determine the convergence or divergence.

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____ 11. Use the Limit Comparison Test (if possible) to

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____ 15. Identify the interval of convergence of a power

15. Identify the interval of convergence of a power series . a. b. c. d. e. 16. Explain how to use the geometric series to find the series for the function . a. replace x with b. replace x with (-x) and multiply the series by 9 c. replace x.

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____ 15. Identify the interval of convergence of a power

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____ 11. Find the fourth degree Maclaurin polynomial for the

11. Find the fourth degree Maclaurin polynomial for the function. a. b. c. d. e. 12. Find the Maclaurin polynomial of degree two for the function f(x) = sec (11x). a. b. c. d. e. 13. Find the third Taylor polynomial for , expanded about c = 1. a. b..

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____ 11. Find the fourth degree Maclaurin polynomial for the

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____ 11. Use Theorem 9.11 to determine the convergence or

11. Use Theorem 9.11 to determine the convergence or divergence of the series. a. diverges b. converges c. Theorem 9.11 inconclusive 12. Use Theorem 9.11 to determine the convergence or divergence of the series. a. converges b. diverges c. Theorem 9.11 inconclusive 13. Sketch the graph of the sequence of partial sum of the series.

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____ 11. Use Theorem 9.11 to determine the convergence or

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____ 11. Use the power series to determine a

11. Use the power series to determine a power series centered at 0 for the function . a. b. c. d. e. 12. Identify the interval of convergence of a power series . a. b. c. d. e. 13. Use the series for to approximate the value.

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____ 11. Use the power series to determine a

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____ 11. Determine the convergence or divergence of the series

11. Determine the convergence or divergence of the series using any appropriate test. a. converges b. diverges 12. Identify the most appropriate test to be used to determine whether the series converges or diverges. a. Ratio Test b. ?-Series Test c. Alternating Series Test d. Telescoping Series Test e. Root Test 13. Determine the.

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____ 11. Determine the convergence or divergence of the series

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11. Solve a. b. c. d. e. 12. Find the

11. Solve a. b. c. d. e. 12. Find the definite integral. a. 2/81 b. - 2/81 c. - 4/9 d. - 2/9 e. 4/9 13. Evaluate Round your answer to three decimal places. a. b. c. d. e. 14. Find a. b. c. d. e. 15. Suppose a damping force affects the vibration of a.

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11. Solve a. b. c. d. e. 12. Find the

Calculus

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6. Find the indefinite integral. a. b. c. d. e. 7.

6. Find the indefinite integral. a. b. c. d. e. 7. Find the indefinite integral. a. b. c. d. e. 8. Find the indefinite integral. a. b. c. d. e. 9. Find the indefinite integral. a. b. c. d. e. 10. Find the indefinite integral. a. b. c. d. e. .

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6. Find the indefinite integral. a. b. c. d. e. 7.

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____ 11. Determine the minimal number of terms required to

11. Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007. a. 5 b. 4 c. 2 d. 6 e. 3 12. Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.004. a. 10 b..

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____ 11. Determine the minimal number of terms required to

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____ 11. Find the Maclaurin series for the function . a.

11. Find the Maclaurin series for the function . a. b. c. d. e. 12. Use a power series to approximate the value of the integral with an error of less than 0.01. Round your answer to two decimal places. a. 0.81 b. 0.74 c. 0.89 d. 0.88 e. 0.84 13. Use a.

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____ 11. Find the Maclaurin series for the function . a.

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11. A hydraulic cylinder an industrial machine pushes a steel

11. A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet (0 ? x ? 4), where the variable force required is F(x) = 3000xe-x pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer.

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11. A hydraulic cylinder an industrial machine pushes a steel

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11. Solve the differential equation a. b. c. d. e.

11. Solve the differential equation a. b. c. d. e. 12. Evaluate the definite integral a. 4 b. 7 c. 5 d. 0 e. 8 13. Find the definite integral. a. 64 b. 56 c. 8 d. 104 e. 7 14. Find the definite integral. a. b. c. d. e. 15. Find the indefinite integral. a. b. c. d. e. .

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11. Solve the differential equation a. b. c. d. e.

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____ 6. Consider the function , and its second-degree polynomial

6. Consider the function , and its second-degree polynomial . Compute the value of f(0.8) and P2(0.8) Round your answer to four decimal places. a. b. c. d. e. 7. Find the Maclaurin polynomial of degree 4 for the function. a. b. c. d. e. 8. Find the Maclaurin.

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____ 6. Consider the function , and its second-degree polynomial

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____ 6. Match the sequence with its graph. a. b. c. d. e.

6. Match the sequence with its graph. a. b. c. d. e. 7. Match the sequence with its graph. a. b. c. d. e. 8. Write the next two apparent terms of the sequence a. b. c. d. e. 9. Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find.

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____ 6. Match the sequence with its graph. a. b. c. d. e.

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9.10 Taylor and Maclaurin Series Multiple Choice Identify the choice that best

9.10 Taylor and Maclaurin Series Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use the definition to find the Taylor series (centered at c) for the function. a. b. c. d. e. 2. Use the definition to find the Taylor series centered at for.

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9.10 Taylor and Maclaurin Series Multiple Choice Identify the choice that best

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6. Find the indefinite integral. a. b. c. d. e. 7.

6. Find the indefinite integral. a. b. c. d. e. 7. Find the indefinite integral. a. b. c. d. e. 8. Find the indefinite integral. a. b. c. d. e. 9. Find the indefinite integral. a. b. c. d. e. 10. Find the indefinite integral. a. b. c. d. e. .

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6. Find the indefinite integral. a. b. c. d. e. 7.

Calculus

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____ 16. Determine the convergence or divergence of the series

16. Determine the convergence or divergence of the series using any appropriate test. a. converges b. diverges 17. Identify the most appropriate test to be used to determine whether the series converges or diverges. a. Limit Comparison Test with b. Ratio Test c. Direct Comparison Test with d. Root Test e. Alternating.

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____ 16. Determine the convergence or divergence of the series

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____ 6. Determine whether the series converges absolutely, converges

6. Determine whether the series converges absolutely, converges conditionally, or diverges. a. converges conditionally b. diverges c. converges absolutely 7. Determine whether the series converges conditionally or absolutely, or diverges. a. The series converges absolutely. b. The series diverges. c. The series converges absolutely but does not converge conditionally. d. The series converges conditionally.

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____ 6. Determine whether the series converges absolutely, converges

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____ 16. Use the Direct Comparison Test to determine the

16. Use the Direct Comparison Test to determine the convergence or divergence of the series . a. The series diverges. b. The series converges. 17. Use the polynomial test to determine whether the series converges or diverges. a. The series diverges. b. The series converges. 18. Use the.

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____ 16. Use the Direct Comparison Test to determine the

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____ 6. Use the binomial series to find the Maclaurin

6. Use the binomial series to find the Maclaurin series for the function . a. b. c. d. e. 7. Use the binomial series to find the Maclaurin series for the function a. b. c. d. e. 8. Use the binomial series to find the Maclaurin series for the.

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____ 6. Use the binomial series to find the Maclaurin

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9.4 Comparisons of Series Multiple Choice Identify the choice that best completes

9.4 Comparisons of Series Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges. a. converges b. diverges 2. Use the Direct Comparison Test to determine the convergence or divergence of the series.

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9.4 Comparisons of Series Multiple Choice Identify the choice that best completes

Calculus

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____ 6. Use the Integral Test to determine the convergence

6. Use the Integral Test to determine the convergence or divergence of the series. a. diverges b. Integral Test inconclusive c. converges 7. Use the Integral Test to determine the convergence or divergence of the series. a. diverges b. converges c. Integral Test inconclusive 8. True or false: The series converges. a. true b. false 9..

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____ 6. Use the Integral Test to determine the convergence

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9.5 Alternating Series Multiple Choice Identify the choice that best

9.5 Alternating Series Multiple Choice Identify the choice that best completes the statement or answers the question. 1. True or false: The series converges. a. true b. false 2. True or false: The series diverges. a. true b. false 3. True or false: The series converges. a. false b. true 4. True.

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9.5 Alternating Series Multiple Choice Identify the choice that best

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6. Determine whether the improper integral diverges or converges. Evaluate

6. Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. a. diverges b. converges 7. Determine whether the improper integral diverges or converges. a. diverges b. converges 8. Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. a. 3 b. 2/3 c. 3/2 d. 2 e. diverges 9. Determine whether the.

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6. Determine whether the improper integral diverges or converges. Evaluate

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9.7 Taylor Polynomials and Approximations Multiple Choice Identify the choice that best

9.7 Taylor Polynomials and Approximations Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find a first-degree polynomial function P1 whose value and slope agree with the value and slope of . a. b. c. d. e. 2. Use a graphing utility to graph and.

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9.7 Taylor Polynomials and Approximations Multiple Choice Identify the choice that best

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____ 16. Suppose an electronic games manufacturer producing a new

____ 16. Suppose an electronic games manufacturer producing a new product estimates the annual sales to be 4,000 units. Each year 20% of the units that have been sold will become inoperative. So, 4,000 units will be in use after 1 year, units will be in use after 2.

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____ 16. Suppose an electronic games manufacturer producing a new

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9.9 Representation of Functions by Power Series Multiple Choice Identify the choice

9.9 Representation of Functions by Power Series Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find a geometric power series for the function centered at 0. a. b. c. d. e. 2. Find a geometric power series for the function centered at 0. a..

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9.9 Representation of Functions by Power Series Multiple Choice Identify the choice

Calculus

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___ 6. Find a power series for the function

_ 6. Find a power series for the function centered at 0. a. b. c. d. e. 7. Find a power series for the function centered at 0. a. b. c. d. e. __ 8. Find a power series for the function centered at 0. a. b. c. d..

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___ 6. Find a power series for the function

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____ 11. Write an expression for the nth term of

11. Write an expression for the nth term of the sequence 10, 22, 34, 46…. a. 24n + 2 b. 12n - 2 c. 10n + 12 d. 12n + 2 e. 14n – 12 12. Write an expression for the nth term of the sequence a. b. c. d. e. 13. Consider.

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____ 11. Write an expression for the nth term of

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____ 11. Write an equivalent series of the series

11. Write an equivalent series of the series with the index of summation beginning at n = 5. a. b. c. d. e. 12. Consider the function given by . Find the interval of convergence for f’(x). a. b. c. d. e. 13. Consider the function given by.

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____ 11. Write an equivalent series of the series

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8.2 Integration by Parts Multiple Choice 1. Find the indefinite integral. a. b.

8.2 Integration by Parts Multiple Choice 1. Find the indefinite integral. a. b. c. d. e. 2. Find the indefinite integral. a. b. c. d. e. 3. Find the indefinite integral. a. b. c. d. e. 4. Find the indefinite integral. a. b. c. d. e. 5. Find the indefinite integral. a. b. c. d. e. .

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8.2 Integration by Parts Multiple Choice 1. Find the indefinite integral. a. b.

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11. Evaluate the limit using L'Hopital's Rule if necessary. a.

11. Evaluate the limit using L'Hopital's Rule if necessary. a.

9.8 Power Series Multiple Choice Identify the choice that best

9.8 Power Series Multiple Choice Identify the choice that best

____ 6. Use the Direct Comparison Test to determine the

____ 6. Use the Direct Comparison Test to determine the

Multiple Choice Identify the choice that best completes the statement

Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Write the first five terms of the sequence. a. b. c. d. e. ____ 2. Write the first five terms of the sequence. a. b. c. d. e. ____ 3. Write the first three terms of.

Multiple Choice Identify the choice that best completes the statement

9.2 Series and Convergence Multiple Choice Identify the choice that

9.2 Series and Convergence Multiple Choice Identify the choice that best completes the statement or answers the question. ___ 1. Write the first five terms of the sequence of partial sums. a. b. c. d. e. ____ 2. Write the first five terms of the sequence of partial sums. a. b. c. d..

9.2 Series and Convergence Multiple Choice Identify the choice that

____ 6. Find the interval of convergence of the power

____ 6. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) a. b. c. d. e. ____ 7. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the.

____ 6. Find the interval of convergence of the power

____ 15. Find the positive values of for which the

____ 15. Find the positive values of for which the series converges. a. The series converges for p > 4. b. The series converges for p > 11. c. The series diverges for all positive values of p. d. The series converges for p > 1. e. The series converges for p ? 8. ____.

____ 15. Find the positive values of for which the

6. Use integration tables to find a. b. c. d.

6. Use integration tables to find a. b. c. d. e. 7. Use integration tables to evaluate the integral a. b. c. d. e. 8. Use integration tables to evaluate the integral a. 21 ? b. c. d. e. 9. Use integration tables to evaluate the integral a. b. c. d..

6. Use integration tables to find a. b. c. d.

____ 11. True or false. The series convergent. a. false b.

____ 11. True or false. The series convergent. a. false b.

9.6 The Ratio and Root Test Multiple Choice Identify the choice that

9.6 The Ratio and Root Test Multiple Choice Identify the choice that

8.8 Improper Integrals Multiple Choice 1. Determine whether the improper integral

8.8 Improper Integrals Multiple Choice 1. Determine whether the improper integral

8.7 Indeterminate Forms and L’Hôpital’s Rule Multiple Choice 1. Evaluate the limit

8.7 Indeterminate Forms and L’Hôpital’s Rule Multiple Choice 1. Evaluate the limit

____ 6. Find the sum of the convergent series. a. b.

____ 6. Find the sum of the convergent series. a. b. c. d. e. ____ 7. Find the sum of the convergent series. a. b. c. d. e. ____ 8. Find the sum of the convergent series a. b. c. d. e. ____ 9. Find the sum of the convergent series a..

____ 6. Find the sum of the convergent series. a. b.

11. Determine whether the improper integral diverges or converges. Evaluate

11. Determine whether the improper integral diverges or converges. Evaluate the integral if it converges. a. b. c. diverges d. e. 12. Find the area between the x-axis and the graph of the function a. 2? b. 2 c. 3 d. 3? e. 0 13. Suppose the capitalized cost C is given by where C0 is.

11. Determine whether the improper integral diverges or converges. Evaluate

9.3 The Integral Test and p-Series Multiple Choice Identify the

9.3 The Integral Test and p-Series Multiple Choice Identify the

8.3 Trigonometric Integrals Multiple Choice 1. Find the indefinite integral. a. b. c.

8.3 Trigonometric Integrals Multiple Choice 1. Find the indefinite integral. a. b. c. d. e. 2. Find the indefinite integral. a. b. c. d. e. 3. Find the indefinite integral. a. b. c. d. e. 4. Find the indefinite integral. a. b. c. d. e. 5. Find the indefinite integral. a. b. c. d. e. .

8.3 Trigonometric Integrals Multiple Choice 1. Find the indefinite integral. a. b. c.

6. Find the indefinite integral a. b. c. d. e.

6. Find the indefinite integral a. b. c. d. e. 7. Find the indefinite integral a. b. c. d. e. 8. Find the indefinite integral. a. b. c. d. e. 9. Find the indefinite integral a. b. c. d. e. 10. Solve the differential equation a. b. c. d. e. .

6. Find the indefinite integral a. b. c. d. e.

____ 6. Use the Root Test to determine the convergence

____ 6. Use the Root Test to determine the convergence

6. Evaluate the limit using L'Hopital's Rule if necessary. a.

6. Evaluate the limit using L'Hopital's Rule if necessary. a.

____ 11. Use the Limit Comparison Test (if possible) to

____ 11. Use the Limit Comparison Test (if possible) to

____ 15. Identify the interval of convergence of a power

____ 15. Identify the interval of convergence of a power series . a. b. c. d. e. ____ 16. Explain how to use the geometric series to find the series for the function . a. replace x with b. replace x with (-x) and multiply the series by 9 c. replace x.

____ 15. Identify the interval of convergence of a power

____ 11. Find the fourth degree Maclaurin polynomial for the

____ 11. Find the fourth degree Maclaurin polynomial for the function. a. b. c. d. e. ____ 12. Find the Maclaurin polynomial of degree two for the function f(x) = sec (11x). a. b. c. d. e. ____ 13. Find the third Taylor polynomial for , expanded about c = 1. a. b..

____ 11. Find the fourth degree Maclaurin polynomial for the

____ 11. Use Theorem 9.11 to determine the convergence or

____ 11. Use Theorem 9.11 to determine the convergence or

____ 11. Use the power series to determine a

____ 11. Use the power series to determine a power series centered at 0 for the function . a. b. c. d. e. ____ 12. Identify the interval of convergence of a power series . a. b. c. d. e. ____ 13. Use the series for to approximate the value.

____ 11. Use the power series to determine a

____ 11. Determine the convergence or divergence of the series

____ 11. Determine the convergence or divergence of the series

11. Solve a. b. c. d. e. 12. Find the

11. Solve a. b. c. d. e. 12. Find the definite integral. a. 2/81 b. - 2/81 c. - 4/9 d. - 2/9 e. 4/9 13. Evaluate Round your answer to three decimal places. a. b. c. d. e. 14. Find a. b. c. d. e. 15. Suppose a damping force affects the vibration of a.

11. Solve a. b. c. d. e. 12. Find the

6. Find the indefinite integral. a. b. c. d. e. 7.

6. Find the indefinite integral. a. b. c. d. e. 7. Find the indefinite integral. a. b. c. d. e. 8. Find the indefinite integral. a. b. c. d. e. 9. Find the indefinite integral. a. b. c. d. e. 10. Find the indefinite integral. a. b. c. d. e. .

6. Find the indefinite integral. a. b. c. d. e. 7.

____ 11. Determine the minimal number of terms required to

____ 11. Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007. a. 5 b. 4 c. 2 d. 6 e. 3 ____ 12. Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.004. a. 10 b..

____ 11. Determine the minimal number of terms required to

____ 11. Find the Maclaurin series for the function . a.

____ 11. Find the Maclaurin series for the function . a. b. c. d. e. ____ 12. Use a power series to approximate the value of the integral with an error of less than 0.01. Round your answer to two decimal places. a. 0.81 b. 0.74 c. 0.89 d. 0.88 e. 0.84 ____ 13. Use a.

____ 11. Find the Maclaurin series for the function . a.

11. A hydraulic cylinder an industrial machine pushes a steel

11. A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet (0 ? x ? 4), where the variable force required is F(x) = 3000xe-x pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer.

11. A hydraulic cylinder an industrial machine pushes a steel

11. Solve the differential equation a. b. c. d. e.

Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Write the first five terms of the sequence. a. b. c. d. e. 2. Write the first five terms of the sequence. a. b. c. d. e. 3. Write the first three terms of.

9.2 Series and Convergence Multiple Choice Identify the choice that best completes the statement or answers the question. _ 1. Write the first five terms of the sequence of partial sums. a. b. c. d. e. __ 2. Write the first five terms of the sequence of partial sums. a. b. c. d..

6. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) a. b. c. d. e. 7. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the.

15. Find the positive values of for which the series converges. a. The series converges for p > 4. b. The series converges for p > 11. c. The series diverges for all positive values of p. d. The series converges for p > 1. e. The series converges for p ? 8. .

6. Find the sum of the convergent series. a. b. c. d. e. 7. Find the sum of the convergent series. a. b. c. d. e. 8. Find the sum of the convergent series a. b. c. d. e. 9. Find the sum of the convergent series a..

15. Identify the interval of convergence of a power series . a. b. c. d. e. 16. Explain how to use the geometric series to find the series for the function . a. replace x with b. replace x with (-x) and multiply the series by 9 c. replace x.

11. Find the fourth degree Maclaurin polynomial for the function. a. b. c. d. e. 12. Find the Maclaurin polynomial of degree two for the function f(x) = sec (11x). a. b. c. d. e. 13. Find the third Taylor polynomial for , expanded about c = 1. a. b..

11. Use the power series to determine a power series centered at 0 for the function . a. b. c. d. e. 12. Identify the interval of convergence of a power series . a. b. c. d. e. 13. Use the series for to approximate the value.

11. Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007. a. 5 b. 4 c. 2 d. 6 e. 3 12. Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.004. a. 10 b..

11. Find the Maclaurin series for the function . a. b. c. d. e. 12. Use a power series to approximate the value of the integral with an error of less than 0.01. Round your answer to two decimal places. a. 0.81 b. 0.74 c. 0.89 d. 0.88 e. 0.84 13. Use a.

6. Consider the function , and its second-degree polynomial . Compute the value of f(0.8) and P2(0.8) Round your answer to four decimal places. a. b. c. d. e. 7. Find the Maclaurin polynomial of degree 4 for the function. a. b. c. d. e. 8. Find the Maclaurin.

9.10 Taylor and Maclaurin Series Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Use the definition to find the Taylor series (centered at c) for the function. a. b. c. d. e. 2. Use the definition to find the Taylor series centered at for.

6. Use the binomial series to find the Maclaurin series for the function . a. b. c. d. e. 7. Use the binomial series to find the Maclaurin series for the function a. b. c. d. e. 8. Use the binomial series to find the Maclaurin series for the.

_ 6. Find a power series for the function centered at 0. a. b. c. d. e. 7. Find a power series for the function centered at 0. a. b. c. d. e. __ 8. Find a power series for the function centered at 0. a. b. c. d..

11. Write an expression for the nth term of the sequence 10, 22, 34, 46…. a. 24n + 2 b. 12n - 2 c. 10n + 12 d. 12n + 2 e. 14n – 12 12. Write an expression for the nth term of the sequence a. b. c. d. e. 13. Consider.

11. Write an equivalent series of the series with the index of summation beginning at n = 5. a. b. c. d. e. 12. Consider the function given by . Find the interval of convergence for f’(x). a. b. c. d. e. 13. Consider the function given by.