17. Use series to evaluate the limit correct to three decimal places.
Select the correct answer.
18. Given the series estimate the error in using the partial sum by comparison
with the series .
____ 19. For which positive integers k is the series convergent? Select the correct answer.
a.
b.
c.
d.
e.
____ 20. Which of the given series are absolutely convergent? Select the correct answer.
a.
b.
Answer Key
Stewart – Calculus ET 8e Chapter 11 Form G
____ 1. Find the value of the limit of the sequence defined by
.
Select the correct answer.
a.
b.
c.
d.
e.
2. Determine whether the sequence converges or diverges. If it converges, find the limit.
3. Determine whether the sequence defined by converges or diverges. If it
converges, find its limit.
____ 4. Determine whether the geometric series converges or diverges. If it converges, find its sum.
Select the correct answer.
a. 12
b. Diverges
c. 3
d. 16
Stewart – Calculus ET 8e Chapter 11 Form G
5. Determine whether the given series converges or diverges. If it converges, find its sum.
6. Determine whether the given series converges or diverges. If it converges, find its sum.
7. Determine which one of the p-series below is convergent.
____ 8. How many terms of the series do we need to add in order to find the sum to the indicated
accuracy? Select the correct answer.
a.
b.
c.
d.
e.
9. Find an approximation of the sum of the series accurate to two decimal places.
10. Determine which series is convergent.
____ 11. Find the values of p for which the series is convergent. Select the correct answer.
a.
b.
c.
d.
Stewart – Calculus ET 8e Chapter 11 Form G
12. Find the radius of convergence and the interval of convergence of the power series.
13. Find the interval of convergence of the series.
14. Find the radius of convergence of the series.
____ 15. Find the radius of convergence of the series. Select the correct answer.
a.
b.
c.
d.
e.
16. Find a power series representation for the function.
17. Find a power series representation for
18. Find the Maclaurin series for f (x) using the definition of the Maclaurin series.
Stewart – Calculus ET 8e Chapter 11 Form G
19. For which positive integers k is the series convergent?
____ 20. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Select the correct answer.
a. conditionally convergent
b. absolutely convergent
c. divergent
Stewart – Calculus ET 8e Chapter 11 Form G
Answer Key
Stewart – Calculus ET 8e Chapter 11 Form H
____ 1. Find the value of the limit for the sequence given. Select the correct answer.
a.
b.
c.
d.
e.
2. If $600 is invested at interest, compounded annually, then after n years the investment is
worth dollars. Find the size of investment after 7 years.
3. Determine whether the given series converges or diverges. If it converges, find its sum.
4. Determine whether the geometric series converges or diverges. If it converges, find its sum.
____ 5. A rubber ball is dropped from a height of 8 m onto a flat surface. Each time the ball hits the
surface, it rebounds to 50% of its previous height. Find the total distance the ball travels.
Select the correct answer.
a. 16
b. 24
c. 8
d. 32
6. Determine whether the geometric series converges or diverges. If it converges, find its sum.
7. Determine whether the given series converges or diverges. If it converges, find its sum.
Stewart – Calculus ET 8e Chapter 11 Form H
____ 8. Find all positive values of u for which the series converges. Select the correct answer.
a.
b.
c.
d.
e.
9. Find all values of p for which the series converges.
10. Test the series for convergence or divergence.
11. Find an approximation of the sum of the series accurate to two decimal places.
12. Approximate the sum to the indicated accuracy.
(five decimal places)
Stewart – Calculus ET 8e Chapter 11 Form H
____ 13. Find the radius of convergence and the interval of convergence of the power series. ]
Select the correct answer.
a.
b.
c.
d.
14. Find the radius of convergence and the interval of convergence of the power series.
____ 15. Find the interval of convergence of the series. Select the correct answer.
a.
b.
c.
d. diverges everywhere
e.
16. Find the radius of convergence of the series.
17. Find a power series representation for the function.
Stewart – Calculus ET 8e Chapter 11 Form H
____ 18. Use the power series for to estimate correct to four decimal places.
Select the correct answer.
a.
b.
c.
d.
e.
19. Given the series estimate the error in using the partial sum by comparison
with the series .
____ 20. Evaluate the function by a Taylor polynomial of degree centered at , and
.
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 11 Form H
Answer Key