Taylor's Theorem

Practice Questions

GRE Subject Test: Math › Taylor's Theorem

Questions

8

1

For which of the following functions can the Maclaurin series representation be expressed in four or fewer non-zero terms?

2

Find the interval of convergence for of the Taylor Series $\sum_{n=0}^{\infty }n!(x-5)^n$ .

3

Write out the first four terms of the Taylor series about for the following function:

4

Write out the first three terms of the Taylor series for the following function about :

5

Suppose that the derivative of a function, denoted , can be approximated by the third degree Taylor polynomial, centered at :

$f'(x) \approx 1 + (x-2) + \frac{4}{3} (x-2)^2 + \frac{8}{9}(x-2)^3$

If , find the third degree Taylor polynomial for centered at .

6

Find the first two terms of the Taylor series about for the following function:

7

Let $f(x)=(1+\frac{x}{2})^{1/3}$

Find the the first three terms of the Taylor Series for centered at .

8

Determine the convergence of the Taylor Series for at where $f(x)=\sum_{n=0}^{\infty }\frac{x^n}{n!}$ .

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