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Question: Answered & Verified by Expert
The value of $\lim _{x \rightarrow 2} \int_{2}^{x} \frac{3 t^{2}}{(x-2)} d t$ is
MathematicsLimitsWBJEEWBJEE 2015
Options:
  • A 10
  • B 12
  • C 8
  • D 16
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]
$=3 \times(2)^{2}=12$

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