Home/Differential Calculus/Indeterminate forms/Formula12.2. Indeterminate formsFormulaIn 12.2. Indeterminate formsFormulaCopy LaTeX0⋅∞:f⋅g=f1/g or g1/f0\cdot\infty:\quad f\cdot g=\frac{f}{1/g}\ \text{or}\ \frac{g}{1/f}0⋅∞:f⋅g=1/gf or 1/fgTagsDifferential calculusDerivativeL'Hôpital and indeterminate limitsIndeterminate formsLimitDetailRewrite to apply L'Hôpital.VariablesfffFunctiongggSecond function or inner compositionConditionsf⋅g=f1/g or g1/ff\cdot g=\frac{f}{1/g}\ \text{or}\ \frac{g}{1/f}f⋅g=1/gf or 1/fgRelated topicsIndeterminate limits and L'HôpitalFound an error? Contact us.Related formulasRelatedFormulalimx→∞f(x)g(x)=limx→∞f′(x)g′(x),f(x)g(x)→0/0 or ∞/∞, f,g differentiable in a neighborhood of ∞, g′(x)≠0 on that neighborhood, limx→∞f′(x)g′(x) exists (finite or ±∞)\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{)}x→∞limg(x)f(x)=x→∞limg′(x)f′(x),g(x)f(x)→0/0 or ∞/∞, f,g differentiable in a neighborhood of ∞, g′(x)=0 on that neighborhood, x→∞limg′(x)f′(x) exists (finite or ±∞)Open formulaOpen in sectionRelatedFormula∞−∞:combine algebraically or use conjugates/logarithms\infty-\infty:\quad \text{combine algebraically or use conjugates/logarithms}∞−∞:combine algebraically or use conjugates/logarithmsOpen formulaOpen in sectionRelatedFormula00, 1∞, ∞0:use y=fg, lny=glnf0^0,\ 1^\infty,\ \infty^0:\quad \text{use } y=f^g,\ \ln y=g\ln f00, 1∞, ∞0:use y=fg, lny=glnfOpen formulaOpen in section