Let $f\left( x \right)$ be twice differentiable function such that $f''\left( 0 \right) = 2$. Then, $\mathop {\lim }\limits_{x \to 0} \frac{{2f\left( x \right) - 3f\left( {2x} \right) + f\left( {4x} \right)}}{{{x^2}}}$ is

JEE MATHEMATICS MCQ: LIMITS

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Let

f\left( x \right)

be twice differentiable function such that

f''\left( 0 \right) = 2

. Then,

\lim\limits_{x \to 0} \frac{{2f\left( x \right) - 3f\left( {2x} \right) + f\left( {4x} \right)}}{{{x^2}}}

View answer and explanation

Correct option: A

Option A (6) is correct because by applying L'Hôpital's Rule twice and using the given condition

f''(0) = 2

, the limit evaluates to 6.

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