WBJEE · Maths · Limits
The value of \(\lim _{x \rightarrow 2} \int_{2}^{x} \frac{3 t^{2}}{(x-2)} d t\) is
- A 10
- B 12
- C 8
- D 16
Answer & Solution
Correct Answer
(B) 12
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 2} \int_{2}^{x} \frac{3 t^{2}}{(x-2)}\) 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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