Home/Differential Calculus/L'Hôpital and indeterminate limits/Indeterminate formsSection 12.2Indeterminate 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/fgRewrite to apply L'Hôpital.f⋅g=f1/g or g1/ff\cdot g=\frac{f}{1/g}\ \text{or}\ \frac{g}{1/f}f⋅g=1/gf or 1/fgView detail →FormulaCopy LaTeX∞−∞:combine algebraically or use conjugates/logarithms\infty-\infty:\quad \text{combine algebraically or use conjugates/logarithms}∞−∞:combine algebraically or use conjugates/logarithmscombine algebraically or use conjugates/logarithms\text{combine algebraically or use conjugates/logarithms}combine algebraically or use conjugates/logarithmsView detail →FormulaCopy LaTeX00, 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=glnfuse y=fg, lny=glnf\text{use } y=f^g,\ \ln y=g\ln fuse y=fg, lny=glnfView detail →
FormulaCopy 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/fgRewrite to apply L'Hôpital.f⋅g=f1/g or g1/ff\cdot g=\frac{f}{1/g}\ \text{or}\ \frac{g}{1/f}f⋅g=1/gf or 1/fgView detail →
FormulaCopy LaTeX∞−∞:combine algebraically or use conjugates/logarithms\infty-\infty:\quad \text{combine algebraically or use conjugates/logarithms}∞−∞:combine algebraically or use conjugates/logarithmscombine algebraically or use conjugates/logarithms\text{combine algebraically or use conjugates/logarithms}combine algebraically or use conjugates/logarithmsView detail →
FormulaCopy LaTeX00, 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=glnfuse y=fg, lny=glnf\text{use } y=f^g,\ \ln y=g\ln fuse y=fg, lny=glnfView detail →