When calculating some limits, it may lead to indeterminate forms which means evaluating the limit directly is not possible. Some of these forms can be worked around by rearranging, and for some we can use L'Hôpital's Rule.
The two main indeterminate forms that we can use l'hopital on are:
Other indeterminate forms exist, such as $0 \cdot \infty$, $\infty - \infty$, $0^0$, $1^\infty$, and $\infty^0$, but not all can be used with L'Hôpital's Rule.
But some forms can be rearranged to match the ones listed above!
L'Hôpital's Rule states that for functions $f(x)$ and $g(x)$ that are differentiable near a point $a$, if the limit $\lim_{x \to a} \frac{f(x)}{g(x)}$ results in an indeterminate form of type $\frac{0}{0}$ or $\frac{\infty}{\infty}$, then:
$$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$$
provided that the limit of the ratio of derivatives exists or is infinite.
L'Hôpital's Rule can also be applied when $a$ is $\infty$ or $-\infty$.
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