Find the Taylor series of f(x)=exf(x) = e^xf(x)=ex centered at a=2a=2a=2.
∑n=0∞e2(x−2)nn!\sum_{n=0}^{\infty} \frac{e^2 (x-2)^n}{n!}∑n=0∞n!e2(x−2)n
∑n=0∞ex(x−2)nn!\sum_{n=0}^{\infty} \frac{e^x (x-2)^n}{n!}∑n=0∞n!ex(x−2)n
∑n=0∞(x−2)nn!\sum_{n=0}^{\infty} \frac{(x-2)^n}{n!}∑n=0∞n!(x−2)n
∑n=0∞2n(x−2)nn!\sum_{n=0}^{\infty} \frac{2^n (x-2)^n}{n!}∑n=0∞n!2n(x−2)n