2) ] } , x->8...

anjutkapanova @anjutkapanova

July 2022 1 8 Report

lim { [ (x)^1/3 -2 ] / [ (x)^1/2 - 2 (2^1/2) ] } , x->8

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ShirokovP

Verified answer

$\lim_{x \to {8}} \frac{ \sqrt[3]{x}-2 }{ \sqrt{x} -2 \sqrt{2} } =[0/0]= \\ \\ =\lim_{x \to {8}} \frac{ (\sqrt[3]{x}-2)' }{ (\sqrt{x} -2 \sqrt{2})' }=\lim_{x \to {8}} \frac{ \frac{1}{3 \sqrt[3]{x^2} } }{ \frac{1}{2 \sqrt{x} } }=\lim_{x \to {8}} { \frac{2 \sqrt{x} }{3 \sqrt[3]{x^2} }= \\ \\ \frac{ \sqrt{2} }{3}$

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