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!

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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