lim-x-2-2x-4-1-3-2-x-2-x-2-

Question Number 102034 by Study last updated on 06/Jul/20

l i \underset{x \to 2}{m} \frac{\sqrt[3]{2 x + 4} - 2}{x^{2} - x - 2} = ?

Answered by Dwaipayan Shikari last updated on 06/Jul/20

\lim_{x \to 2} \frac{\sqrt[3]{2 x + 4} - 2}{2 x + 4 - 8} . \frac{2 x - 4}{(x - 2) (x + 1)} = \frac{1}{3} 8^{\frac{- 2}{3}} . \frac{2}{3} = \frac{1}{18}

{\frac{{(2 x + 3)}^{\frac{1}{3}} - {(8)}^{\frac{1}{3}}}{2 x + 4 - 8} = \frac{1}{3} 8^{- \frac{2}{3}}

o r y o u c a n u s e L h o s p i t a l

Commented by Study last updated on 06/Jul/20

w h a t i s t h e f u r m o l l a h ?

Answered by bemath last updated on 06/Jul/20

\lim_{x \to 2} \frac{1}{(x + 1)} . \lim_{x \to 2} \frac{\sqrt[3]{2 x + 4} - 2}{x - 2} =

\frac{1}{3} . \lim_{x \to 2} \frac{2}{3 \sqrt[3]{{(2 x + 4)}^{2}}} =

\frac{2}{9 \times 4} = \frac{1}{18}

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