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

Question

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

anonymous · Answer

converges everywhere
do you know the expansion of $e^x$? substitute $2x^2$ for $x$

anonymous · Answer

unfortunately i dont know it

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

now it should be easy right? make the substitution

anonymous · Answer

hmm..

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

*dont learned math since so long

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

aah it was a complete answer?

anonymous · Answer

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