QJEEM21Ma0eac: JEE Main 2021 Mathematics - Class 12 JEEM21Ma0eac Solution: Let f(x) be a differentiable function at x = a with f'(a) = 2…

Question

Verified Solution • 2025–26 Session moderate

Let f(x) be a differentiable function at x = a with f'(a) = 2 and f(a) = 4.

Then

lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}

equals :

Accepted Answer

L = lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}

[

\frac{0}{0}

form]

Using L' Hospital rule we get

L = lim_{x \to a} \frac{f (a) - a f^{'} (x)}{1}

f (a) - a f^{'} (a) = 4 - 2 a

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