find-lim-x-0-x-e-lnx-

Question Number 32990 by abdo imad last updated on 09/Apr/18

f i n d {l i m}_{x \to 0^{+}} x e^{- l n x} .

Commented by prof Abdo imad last updated on 09/Apr/18

t h e c h . l n x = - t g i v e

{l i m}_{x \to 0^{+}} x e^{- l n x} = {l i m}_{t \to + \infty} e^{- t} . e^{t} = e^{0} = 1

Answered by kyle_TW last updated on 09/Apr/18

\underset{x \to 0^{+}}{l i m x} \cdot \frac{1}{e^{l n x}} = \underset{x \to 0^{+}}{l i m x} \cdot \frac{1}{x} = 1

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