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lim-x-0-xln-sinx-




Question Number 132226 by kaivan.ahmadi last updated on 12/Feb/21
lim_(x→0^+ )   xln(sinx)
$${li}\underset{{x}\rightarrow\mathrm{0}^{+} } {{m}}\:\:{xln}\left({sinx}\right) \\ $$
Answered by Olaf last updated on 12/Feb/21
sinx ∼_0  x  ⇒ lim_(x→0)  xln(sinx) = lim_(x→0)  xlnx = 0
$$\mathrm{sin}{x}\:\underset{\mathrm{0}} {\sim}\:{x} \\ $$$$\Rightarrow\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}\mathrm{ln}\left(\mathrm{sin}{x}\right)\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}\mathrm{ln}{x}\:=\:\mathrm{0} \\ $$

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