Other Indeterminate Expressions: Find the indicated limits. You may have to manipulate your expression before the applying the Rule of L'Hopital. Enter the letter "D" if the limit does not exist.
Suppose $p(x)$ is a polynomial of degree greater than 0. Then
$\displaystyle\lim_{x\longrightarrow \infty} \frac{ p(x)}{e^x} =$ and
$\displaystyle\lim_{x\longrightarrow \infty} \frac{ p(x)}{\ln x} =$ .

$\displaystyle\lim_{x\longrightarrow 0} \left(1+x\right)^{1/x} =$ .
$\displaystyle\lim_{x\longrightarrow \infty} \left(1+\frac{1}{x}\right)^{x} =$ .
$\displaystyle\lim_{x\longrightarrow \infty} \left(1+\frac{1}{x}\right)^{2x} =$ .
$\displaystyle\lim_{x\longrightarrow 0^+} x^x =$ .
$\displaystyle\lim_{x\longrightarrow 0^+} x^{\displaystyle x^x} =$ .