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Calculus II (MAT-232)

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Written Assignment 5

* *

* *

Answer all assigned exercises, and show all work. Each exercise is worth 5 points.

*Submitting a graph is not required; however, you are encouraged to create one for your own benefit and to include (or describe) one if possible.

Section 8.6

4. Determine the radius and interval of convergence.

10. Determine the radius and interval of convergence.

12. Determine the radius and interval of convergence.

16. Determine the radius and interval of convergence.

24. Determine the interval of convergence and the function to which the given power series converges.

26. Find a power series representation of *f*(*x*) about *c* = 0 (refer to example 6.6). Also, determine the radius and interval of convergence, and graph *f*(*x*) together with the partial sums and .

28. Find a power series representation of *f*(*x*) about *c* = 0 (refer to example 6.6). Also, determine the radius and interval of convergence, and graph *f*(*x*) together with the partial sums and .

Section 8.7

4. Find the Maclaurin series (i.e., Taylor series about *c* = 0) and its interval of convergence.

6. Find the Maclaurin series (i.e., Taylor series about *c* = 0) and its interval of convergence.

10. Find the Taylor series about the indicated center, and determine the interval of convergence.

14. Find the Taylor series about the indicated center, and determine the interval of convergence.

22. Prove that the Taylor series converges to *f*(*x*) by showing that .

24. Prove that the Taylor series converges to *f*(*x*) by showing that .

30. Use a known Taylor series to find the Taylor series about *c* = 0 for the given function, and find its radius of convergence.

Section 8.8

4. Use an appropriate Taylor series to approximate the given value, accurate to within .

8. Use a known Taylor series to conjecture the value of the limit.

12. Use a known Taylor series to conjecture the value of the limit.

16. Use a known Taylor polynomial with *n* nonzero terms to estimate the value of the integral.

18. Use a known Taylor polynomial with *n* nonzero terms to estimate the value of the integral.

24. Use the Binomial Theorem to find the first five terms of the Maclaurin series.

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