Search any question & find its solution
Question:
Answered & Verified by Expert
The value of $\lim _{x \rightarrow 2} \int_{2}^{x} \frac{3 t^{2}}{(x-2)} d t$ is
Options:
Solution:
1587 Upvotes
Verified Answer
The correct answer is:
12
$\lim _{x \rightarrow 2} \int_{2}^{x} \frac{3 t^{2}}{(x-2)}$ dt $=\frac{\lim _{x \rightarrow 2} \int_{2}^{x} 3 t^{2} d t}{\lim _{x \rightarrow 2}(x-2)}$
$=\frac{\lim _{x \rightarrow 2} 3 x^{2}}{1} \quad$ [using L' Hospital's nule]
$=3 \times(2)^{2}=12$
$=\frac{\lim _{x \rightarrow 2} 3 x^{2}}{1} \quad$ [using L' Hospital's nule]
$=3 \times(2)^{2}=12$
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.