If $f\left( x \right)$ is differentiable function and $f''\left( 0 \right) = a$, then $\mathop {\lim }\limits_{x \to 0} \frac{{2f\left( x \right) - 3f\left( {2x} \right) + f\left( {4x} \right)}}{{{x^2}}}$ is equal to

JEE MATHEMATICS MCQ: LIMITS

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f\left( x \right)

is differentiable function and

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

, then

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

is equal to

View answer and explanation

Correct option: A

3a

Option A (

3a

) is the correct answer because it is obtained by applying L'Hopital's rule twice and then evaluating the limit.

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