Name:

College ID:

Thomas Edison State College

Calculus II (MAT-232)

Section no.:

Semester and year:

**Written Assignment 5**

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

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*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.

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**Section 8.6**

**4.** **Determine the radius and interval of convergence.**

**10.** **Determine the radius and interval of convergence.**

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**12.** **Determine the radius and interval of convergence.**

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**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.**

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

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

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

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

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

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

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**Section 8.8**

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**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.**

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

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

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

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

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