Taylor Series Test

1.  Find the radius of convergence of the power series

•   $\frac{1}{4}$  

•  $\frac{1}{2}$  

• 2

• 0

•  $\infty$  

What are all the values of x for which the series converges?

• $-\frac{11}{2}<x<\frac{1}{2}$

• $-\frac{11}{2}\le x\le\frac{1}{2}$

• 
• $\left(-\infty,\ \infty\right)$

• $-\frac{11}{2}\le x<\frac{1}{2}$

This power series converges conditionally at x = 7. Which of the following statements about the convergence of the series at x = -2 is true ?

• The series converges absolutely at x = -2.

• The series converges conditionally at x =-2.

• The series diverges at x =-2.

• There is not enough information to determine the convergence of the series at x = -2.

 $-1+6\left(x-1\right)-24\left(x-1\right)^2+80\left(x-1\right)^3.$  This is a third-degree Taylor polynomial for a function f about        x = 1. What is the value of    $f'''\left(1\right)$   ?

•  $\frac{40}{3}$  

•  $\frac{80}{3}$  

• 80

• 240

• 480

The third order Taylor polynomial about x = 0 of ln(1-2x) is

• 
• 
• 
• 
• 

 If a fifth degree Taylor Polynomial centered at x =2  is used to approximate f(4), and  $\left|f\left(4\right)-T_5\left(4\right)\right|\le B$  , which of the following could be B if the graph shown is a portion of the graph of  $f^{\left(6\right)}\left(x\right).$  .  

•  $\frac{8}{3}$  

•  $\frac{16}{3}$  

• 4.8

• 1.6

• 1.956

What are the first three terms of the series.

• $\frac{x^5}{2}-\frac{x^7}{6}+\frac{x^9}{10}+C$

• $\frac{x^5}{2}-\frac{2x^7}{3}+\frac{8x^9}{5}+C$

• $\frac{2x^5}{5}-\frac{8x^7}{21}+\frac{4x^9}{5}+C$

• $\frac{2x^5}{5}-\frac{2x^7}{21}+\frac{2x^9}{45}+C$

• $\frac{2x^5}{5}-\frac{x^6}{3}+\frac{8x^7}{21}+C$

Find a power series for

• 
• 
• 
• 

What are all the values for which this series converges?

• $\left(-\infty,\ \infty\right)$

• 
• {4}

• It never converges

• (-1, 9)

Using the Maclaurin series for  $\frac{1}{1+x^3}$ , find the coefficient of the  $x^{13\ }$ term in the series  $\int_{ }^{ }\frac{x^3}{1+x^3}dx$  . 

•  $-\frac{1}{13}$  

•  $-\frac{1}{40}$  

•  $\frac{1}{13}$  

•  $\frac{1}{40}$  

• none of these