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L'Hôpital's Rule

From AoPSWiki

L'Hopital's Rule is a theorem dealing with limits that is very important to calculus.

Contents

Theorem

The theorem states that for real functions f(x),g(x), if \lim f(x),g(x)\in \{0,\pm \infty\} \lim\frac{f(x)}{g(x)}=\lim\frac{f'(x)}{g'(x)} Note that this implies that \lim\frac{f(x)}{g(x)}=\lim\frac{f^{(n)}(x)}{g^{(n)}(x)}=\lim\frac{f^{(-n)}(x)}{g^{(-n)}(x)}

Proof

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Problems

Introductory

Intermediate

Olympiad

See Also

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