Calculus

# L'Hopital's Rule - Problem Solving

If $\displaystyle f(x) = \sum_{k=1}^{n} x^k$, what is the value of $\displaystyle \lim_{n \to \infty} \frac{9n^2 + 10n + 11}{f'(1)} ?$

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

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