Formula

Tags

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

Detail

Variables

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

Conditions

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

Related topics

• Indeterminate limits and L'Hôpital

Related formulas

• Related

  Formula

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

• Related

  Formula

  $$0\cdot\infty:\quad f\cdot g=\frac{f}{1/g}\ \text{or}\ \frac{g}{1/f}$$
  Open formulaOpen in section