Formula

Tags

• Differential calculus
• Derivative
• L'Hôpital's rule
• Limit

Detail

Explore the idea

Variables

• $x$Independent variable
• $a$Point or real constant
• $f$Function
• $g$Second function or inner composition
• $f'$Derivative of $f$

Conditions

• $\frac{f(x)}{g(x)}\to 0/0\text{ or }\infty/\infty,\ f,g\text{ differentiable in a punctured neighborhood of }a,\ g'(x)\neq 0\text{ on that neighborhood},\ \lim_{x\to a}\frac{f'(x)}{g'(x)}\ \text{exists (finite or }\pm\infty\text{)}$

Frequently asked questions

When can I apply L'Hôpital's rule?

When the limit has indeterminate form $0/0$ or $\infty/\infty$, the functions are differentiable near the point and $g'\neq0$ in a neighborhood (except possibly at the point).

Also known as

• L'Hôpital
• L'Hospital
• indeterminate limit

Related topics

• Indeterminate limits and L'Hôpital

Related formulas

• Related

  Formula

  $$\lim_{x\to\infty}\frac{f(x)}{g(x)}=\lim_{x\to\infty}\frac{f'(x)}{g'(x)},\qquad \frac{f(x)}{g(x)}\to 0/0\text{ or }\infty/\infty,\ f,g\text{ differentiable in a neighborhood of }\infty,\ g'(x)\neq 0\text{ on that neighborhood},\ \lim_{x\to\infty}\frac{f'(x)}{g'(x)}\ \text{exists (finite or }\pm\infty\text{)}$$
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