I'm blanking out, how would I show either a sequential limit or epsilon-delta proof for this? For the sequential limit definition, is it an obvious property that if $\displaystyle \lim_{n\to \infty} x_{n} = x$, then $\displaystyle \lim_{n\to \infty} 2^{x_{n}} = 2^{x}$. If not, how do I go about proving that, or how would I show an epsilon-delta proof? I am completely stuck on how it could be shown using epsilon-delta. Thanks.