Find the Taylor series centered at $c = -1$.
$f(x) = e^{4x}$
Identify the correct expansion.
$\sum_{n=0}^{\infty} \frac{4^n}{n!}(x+1)^n$
$\sum_{n=0}^{\infty} \frac{4^{n-4}}{n!}(x+1)^n$
$\sum_{n=0}^{\infty} \frac{x^n e^{-4}}{n!}$
$\sum_{n=0}^{\infty} \frac{4^n e^{-4}}{n!}(x+1)^n$
Find the interval on which the expansion is valid.
(Give your answer as an interval in the form (*,*). Use the symbol $\infty$ for infinity, $\cup$ for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed. Enter $\emptyset$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)
interval:
