Taylor and Maclaurin series

• 1/4

• -1

• 1/2

• -2

• 1

1.  Find the radius of convergence of the power series

•   $\frac{1}{4}$  

•  $\frac{1}{2}$  

• 2

• 0

•  $\infty$  

• -2/3

• -4/3

• 4/3

• -8/3

• 2/3

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

• $-\frac{11}{2}<x<\frac{1}{2}$

• $-\frac{11}{2}\le x\le\frac{1}{2}$

• 
• $\left(-\infty,\ \infty\right)$

• $-\frac{11}{2}\le x<\frac{1}{2}$

 $-1+6\left(x-1\right)-24\left(x-1\right)^2+80\left(x-1\right)^3.$  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

What are the first three terms of the series.

Find a power series for

• 
• 
• 
• 

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

Which of the following is a power series expansion for  $\frac{x^2}{1-x^2}$  

•  $1+x^2+x^4+x^6+x^8+...$  

•  $x^2+x^3+x^4+x^5+...$  

•  $x^2+2x^3+3x^4+4x^5+...$  

•  $x^2+x^4+x^6+x^8+...$  

•  $x^2-x^4+x^6-x^8+...$  

• Converges