How do I find the limit of the function? How do I find the limit for the function $(1 + h)^{\frac{1}{h}}$ as $h$ goes to $0$? I do not know where to start. We just started using Logs.

Write $$(1+h)^{\frac{1}{h}}=e^{\frac{1}{h} \ln{(1+h)}}$$
So what is the limit $\frac{1}{h}\ln{(1+h)}$ as $h \to 0$?
Take  the function $f(h)=\ln(1+h)$ and we have $f(0)=0$
Then $$\lim_{h \to 0} \frac{\ln(1+h)}{h}=\lim_{h \to 0}\frac{f(h)-f(0)}{h-0}=f'(0)=1$$
Thus the general limit is $e$
