# L’Hopital’s Rule Problems and solutions

In calculus, the limits of some functions become indeterminate. For solving the limits of such functions, the L’Hospital’s Rule is used. Here is the list of limit problems with easily understandable solutions to learn how to find the limits of the functions by the L’Hopital’s Rule.

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{1-\cos{mx}}{1-\cos{nx}}}$

Find $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{e^{3\normalsize +\large x}-\sin{x}-e^3}{x}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 3}{\normalsize \dfrac{\sqrt{3x}-3}{\sqrt{2x-4}-\sqrt{2}}}$

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{\log_{\displaystyle e}{\big(\cos{(\sin{x})}\big)}}{x^2}}$

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