MCQ
$\lim_{x \rightarrow 2}\frac{\sqrt[3]{3x+2}-2}{\sqrt[5]{x+30}-2}=$
- A$10$
- ✓$20$
- C$30$
- D$40$
$\lim_{x \rightarrow 2} \frac{\sqrt[3]{3x+2}-2}{\sqrt[5]{x+30}-2}$
$\lim_{x\rightarrow 2}\frac{(3x+2)^{\frac{1}{3}}-2}{(x+30)^{\frac{1}{5}}-2}\ \ \ \ (\frac{0}{0}) from L' \ hospital \ rule $
$\lim_{x\rightarrow 2}\frac{\frac{1}{3}(3x+2)^{\frac{-2}{3}}.3}{\frac{1}{5}(x+30)^{\frac{-4}{5}}} $
$ = \frac{\frac{1}{4}}{\frac{1}{5}.\frac{1}{16}}=\frac{1}{4}\times5\times16=20$
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