Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

If f(x) is differentiable at x = a, then $\lim\limits_{x \rightarrow a} \frac{x^2 f(a)-a^2 f(x)}{x-a}$ is equal to

Options:

$a^2 f(a)-2 a f'(a)$

$2 a f(a)+a^2 f'$

$2 a f(a)-a^2 f'(a)$

none of these

Correct Answer:

$2 a f(a)-a^2 f'(a)$

Explanation:

$\lim\limits_{x \rightarrow a} \frac{x^2 f(a)-a^2 f(x)}{x-a}$

$=\lim\limits_{x \rightarrow a}2xf(a)-a^2f'(x)$ Using L' Hopitals Rule

$=2 a f(a)-a^2 f'(a)$