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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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