a. Differentiate the Taylor series about 0 for the function f(x)=e?2x.

b. Identify the function represented by the differentiated series.

c. Give the interval of convergence of the power series for the derivative.

a. Which of the following is the derivative of the Taylor series about x=?0?

A.

?

k=1

?

(?2)kxk?1(k?1)!

B.

?

k=0

?

xk?1(k?1)!

C.

?2?

k=0

?

xk?1(k?1)!

D.

?2?

k=1

?

xk?1(k?1)!

b. What is the function represented by the differentiated?series?

f(x)=

nothing

c. What is the interval of?convergence?

nothing

nothing

a. Differentiate the Taylor series about 0 for the function f(x) = e - 2x b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Which of the following is the derivative of the Taylor series about x = 0? OA. (-2) Kxk - 1 k - 1 X' (K - 1)! OB. E k = 1 K= 0 ( k - 1 ) ! Oc. -2_ xk - 1 K = 0 (k - 1) ! OD. - 2 _ xk - 1 K = 1 ( k - 1 ) ! b. What is the function represented by the differentiated series? f(x) = c. What is the interval of convergence?