If f : R → R is a differentiable function and f(2) = 6, then \underset{x \rightarrow 2}{Lim} \int_{6}^{f \left(\right. x \left.\right)} \frac{2 t}{\left(\right. x

Engineering

Mathematics

Leibnitz Rule Derivative of Anti Derivatives

Question

If f : R → R is a differentiable function and f(2) = 6, then $\underset{x \to 2}{Lim} \int_{6}^{f (x)} \frac{2 t}{(x - 2)} dt$ is

12f '(2)

24f '(2)

2f '(2)

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$\lim_{x \to \infty} \int_{6}^{f (x)} \frac{2 tdt}{(x - 2)} dx {given that f (2) = 6}$

$\frac{0}{0}$ from, so we use L – Hospital Rule

$\lim_{x \to \infty} \frac{f' (x) . 2 f (x)}{1}$

= f'(2).2f(2)

= 12f’(2)