Calculus
# L'Hôpital's Rule

Evaluate $\displaystyle \lim_{x \to 1} \frac{x^{13} + 10x-11}{x-1}$.

If $\displaystyle \lim_{x \to 0^+} (1+\sin 5 x)^{\cot x} = a$, what is the value of $\ln a$?

Evaluate $\displaystyle \lim_{x \to 0} \frac{1 - \cos (6x)}{x^2}$.

Evaluate $\displaystyle \lim_{x \to 0^+} x \ln x$.