JEE Mains · Maths · STD 11 - 12. limits
If \(f:R \to R\) is a differentiable function and \(f\left( 2 \right) = 6\), then \(\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {\frac{{2\,tdt}}{{\left( {x - 2} \right)}}} \) is
- A \(0\)
- B \(2f'\left( 2 \right)\)
- C \(12f'\left( 2 \right)\)
- D \(24f'\left( 2 \right)\)
Answer & Solution
Correct Answer
(C) \(12f'\left( 2 \right)\)
Step-by-step Solution
Detailed explanation
\(\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {\frac{{2tdt}}{{\left( {x - 2} \right)}}} dx\) {given that \(\,f\left( 2 \right) = 6\)} \(\frac{0}{0}\) from, so we use \(L-\) Hopital Rule…
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