L'Hôpital's Rule

L'Hopital's Rule - Problem Solving


If f(x)=k=1nxk\displaystyle f(x) = \sum_{k=1}^{n} x^k , what is the value of limn9n2+10n+11f(1)?\displaystyle \lim_{n \to \infty} \frac{9n^2 + 10n + 11}{f'(1)} ?

Evaluate limx1x13+10x11x1\displaystyle \lim_{x \to 1} \frac{x^{13} + 10x-11}{x-1}.

If limx0+(1+sin5x)cotx=a\displaystyle \lim_{x \to 0^+} (1+\sin 5 x)^{\cot x} = a, what is the value of lna\ln a?

Evaluate limx01cos(6x)x2\displaystyle \lim_{x \to 0} \frac{1 - \cos (6x)}{x^2}.

Evaluate limx0+xlnx\displaystyle \lim_{x \to 0^+} x \ln x .


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