Limits & Continuity: Let f(x) be a differentiable function at x=a with f'(a)=2 and f(a)=4… | JEE Main 2021 | Yukti Vault

Yukti Vault

JEE Main 2021 (Online) 26th February Evening ShiftQuestion 1

Let $f(x)$ be a differentiable function at $x=a$ with $f'(a)=2$ and $f(a)=4$. Then $\lim_{x\to a}\frac{xf(a)-af(x)}{x-a}$ equals :

Limits & Continuity

$2a-4$$4-2a$✓ Correct answer$2a+4$$a+4$

Solution

Numerator $xf(a)-af(x)=4x-af(x)$ is $0$ at $x=a$. By L'Hopital: $4-af'(a)=4-2a$. Option B.

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