Search any question & find its solution
Question:
Answered & Verified by Expert
$\lim _{x \rightarrow a} \frac{(x+2)^{5 / 3}-(a+2)^{5 / 3}}{x-a}=$
Options:
Solution:
1047 Upvotes
Verified Answer
The correct answer is:
$\frac{5}{3}(a+2)^{2 / 3}$
Apply the L-Hospital's rule, $\lim _{x \rightarrow a} \frac{f(x)}{g(x)}=\lim _{x \rightarrow a} \frac{f^{\prime}(x)}{g^{\prime}(x)}$.
\(\begin{aligned}
& =\lim _{x \rightarrow a} \frac{\frac{5}{3}(x+2)^{2 / 3}}{1 \frac{1}{3}} \\
& =\frac{5}{3}(a+2)^{\frac{2}{3}}
\end{aligned}\)
\(\begin{aligned}
& =\lim _{x \rightarrow a} \frac{\frac{5}{3}(x+2)^{2 / 3}}{1 \frac{1}{3}} \\
& =\frac{5}{3}(a+2)^{\frac{2}{3}}
\end{aligned}\)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.