Question

write the following functions as power series, and calculate their open intervals of convergence
a) \(\exp(2x^{2})\)

Answer 1

converges everywhere
do you know the expansion of \(e^x\)? substitute \(2x^2\) for \(x\)

Answer 2

unfortunately i dont know it

Answer 3

\[\sum_{n=0}^{\infty} \frac{x^{n}}{n!}\] is it ?

Answer 4

yes that is it. need to try to remember this one
also sine and cosine

Answer 5

now it should be easy right? make the substitution

Answer 6

hmm..

Answer 7

\[\sum\frac{(2x^2)^n}{n!}\] clean it up a little

Answer 8

i am sorry i am confused its my second day here, and leraning math since solong :) but math was never so fun before i found this website

Answer 9

*dont learned math since so long

Answer 10

do we gonna use \[|\frac{a_{n+1}}{a_{n}}|\] ?

Answer 11

thats right and R is infinite or for all x is convergence

Answer 12

aah it was a complete answer?