Evaluate the limits, using L’Hôpital’s Rule.

1. $\displaystyle{ \lim_{x\to \infty} \frac{{4x^{4}}}{{e^{x}}} =}$
2. $\displaystyle{ \lim_{x\to \infty} \frac{{10\sqrt{x}}}{{e^{x}}} =}$
3. $\displaystyle{ \lim_{x\to \infty} \frac{{4e^{x}}}{{13\sqrt{x}}} = }$
4. $\displaystyle{ \lim_{x\to \infty} \frac{{e^{x}}}{{2^{x}}} = }$
5. $\displaystyle{ \lim_{x\to \infty} \frac{{e^{x}}}{{8^{x}}} = }$

limit