JEE PYQ: Differentiation Question 4
Question 4 - 2021 (26 Feb Shift 2)
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:
(1) $2a + 4$ (2) $2a - 4$ (3) $4 - 2a$ (4) $a + 4$
Show Answer
Answer: (3) $4 - 2a$
Solution
By L’Hopital’s rule: $L = f(a) - af’(a) = 4 - 2a$.