Calculus Expert Answers & Study Resources

Solve each system by using the Gaussian elimination method. Let   Find each of the following matrices or determinants, if possible. 6. |B| 7. |G| 8. DB 9. 2C - D 10. FE .

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.

____ 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 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.

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..

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.

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.     .

Multiple Choice: Choose the best answer for each problem. 1. A 3 × 2 matrix has: a. 2 rows and 3 columns b. an order of 6 c. 3 rows and 2 columns d. an equivalent 3 × 2 matrix 2. The matrix  is equivalent to which of the following? a. b. c. d. 3. Use matrices.

____ 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..

____ 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. 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.

____ 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..

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.

____ 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.

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.     .

____ 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.

  ____ 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.

____ 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.

____ 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.

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.

Solve each system by using the Gaussian elimination method. Let   Find each of the following matrices or determinants, if possible. 6. G-1 7. |A| 8. BD 9. C + 2D 10. FE .

Solve each system by using the Gaussian elimination method. 1. 2. Let   Find each of the following matrices or determinants, if possible. 3. A – B 4. CA 5. |G| .

____ 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.

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.

____ 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.

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.

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.

___ 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..

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.     .

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.     .

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.     .

11. Cramer's Rule will give the solution for all systems of two linear equations unless: a. the system has a unique solution. b. Dz is zero. c. the coefficient determinant is zero. d. Both HB and HC are zero. 12. Solve using any matrix method: Fifty percent of the boys and sixty percent of the.

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.

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.     .

____ 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.

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..

____ 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.

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.

____ 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.

____ 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.

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.

  ____ 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.

____ 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.

____ 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.

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..

____ 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.

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.

____ 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..

____ 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.

____ 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.