Question

Find the first few terms of the Maclaurin series of:
sin(sqrtx)/(sqrtx)

Answer 1

Im trying to figure out which method to use to solve this.....since taking each derivative takes way too long

Answer 2

yes it does take very long. that's why they only want the first few terms

Answer 3

sin(x)/x is the sinc function: http://en.wikipedia.org/wiki/Sinc_function

Here are are few terms for your function to start you off:

\(1-x/6+x^2/120-x^3/5040+x^4/362880-x^5/39916800+\cdots\)

Take a few differentials, not too bad..

Good Luck.

Answer 4

you want to use known taylor series like ybarrap did. takes a lot less time