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Chapter 8: Q. 55 (page 692)

Find the Maclaurin series for the functions in Exercises 51–60
by substituting into a known Maclaurin series. Also, give the
interval of convergence for the series.
$\frac{1}{8 + x^{3}}$

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Most popular questions from this chapter

Find the interval of convergence for each power series in Exercises 21–48. If the interval of convergence is finite, be sure to analyze the convergence at the endpoints.

$\sum_{k = 0}^{\infty} k! x^{k}$

Find the interval of convergence for power series: $\sum_{k = 0}^{\infty} \frac{{(- 1)}^{k}}{(2 k)!} x^{2 k}$ .

What is a difference between a Taylor polynomial and the Taylor series for a function f at a point $x_{0}$ ?

Use an appropriate Maclaurin series to find the values of the series in Exercises 17–22.

$\sum_{k = 0}^{\infty} \frac{{(- 1)}^{k} π^{2 k + 1}}{(2 k + 1)!}$

What is $x_{0}$ if the interval of convergence for the power series $\sum_{k = 0}^{\infty} a_{k} {(x - x_{0})}^{k} is (2, 10] ?$

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