Evaluate the limits, using L'Hôpital's Rule.
Enter INF for $\infty$, -INF for $-\infty$, or DNE if the limit does not exist, but is neither $\infty$ nor $-\infty$.

a) $\displaystyle \lim_{x\to \infty} \frac{4 x^{4}}{e^x} =$

b) $\displaystyle \lim_{x\to \infty} \frac{10 \sqrt{x}}{e^x} =$

c) $\displaystyle \lim_{x\to \infty} \frac{4 e^x}{13 \sqrt{x}} =$

d) $\displaystyle \lim_{x\to \infty} \frac{e^x}{2^x} =$

e) $\displaystyle \lim_{x\to \infty} \frac{e^x}{8^x} =$