Saturday, 13 June 2015

calculus - Infinity indeterminate form that L'Hopital's Rule: limxto0+fracefrac1xx2



When I tried to find the limit of
lim

by applying L'Hopital's Rule the order of denominator would increase. What else can I do for it?


Answer



Let y = \dfrac{1}{x}, then x = \dfrac{1}{y} \Rightarrow L = \displaystyle \lim_{y \to +\infty} \dfrac{y^2}{e^y}= \displaystyle \lim_{y \to +\infty} \dfrac{2y}{e^y}=\displaystyle \lim_{y \to +\infty} \dfrac{2}{e^y}= 0


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