calculus - How do I approach solving this indeterminate limit? $lim_limits{hto 0}frac{1}{h}lnleft(frac{2+h}{2}right)$

Disclaimer: I am a middle aged adult learning Calculus. This is not a student posting his homework assignment. Thank humanity for this great forum!

$$\lim_\limits{h\to 0}\frac{1}{h}\ln\left(\frac{2+h}{2}\right)$$

1) Can't directly sub the h. So, normally you reduce and cancel. Can you point me in the right direction? The directions say "manipulate the expression so L'Hopital's is used" I think L'hopital's is involved. Just not sure how to deal with the $\frac{1}{h}$

$$\lim_\limits{x\to \infty}\frac{x^k}{e^x}$$

2) Also, any tips on the one above? If $k$ is a positive integer, what is the limit above?

Thanks for any guidance.