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## L'Hôpital's Rule

When you've got a limit that looks like 0/0 or ∞/∞, L'Hôpital's rule can often find its value -- and make it clear that not all infinities are equal!

# 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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