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Question Number 113812 by Khalmohmmad last updated on 15/Sep/20

lim_(x→0) xlnx=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}xlnx}=? \\ $$

Answered by bemath last updated on 15/Sep/20

lim_(x→0)  ((ln x)/(1/x)) = lim_(x→0)  ((1/x)/(−(1/x^2 ))) = 0

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:{x}}{\frac{\mathrm{1}}{{x}}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}}{{x}}}{−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}\:=\:\mathrm{0} \\ $$

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