# Calculus II WA5

**Paper, Order, or Assignment Requirements**

**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**

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

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

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

**Determine the radius and interval of convergence**

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

**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 .**

**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**

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

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

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

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

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

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

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

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

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

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

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

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

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