Define a function sinc(x) (pronounced "sink of x") by: sinc(x)= {sin(x)/x if x is not 0 {1 if x = 0 use this list of basic taylor series to find the taylor series for f(x) = (sinc(x)) based at 0. a. give your answer using summation notation. b. give the interval on which the series converges.

You probably know that

Then

when , and 1 when .

By the ratio test, the series converges if the following limit is less than 1:

The limit is 0, so the series converges for all .

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )