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  4. Let f: R arrow R be a function such that f(2)=4 and f'(2)=1. Then, the value of displaystyle lim x arrow 2 (x2 f(2)-4 f(x)/x-2) is equal to :

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Q. Let $f: R \rightarrow R$ be a function such that $f(2)=4$ and $f'(2)=1$. Then, the value of $\displaystyle\lim _{x \rightarrow 2} \frac{x^{2} f(2)-4 f(x)}{x-2}$ is equal to :

JEE MainJEE Main 2021Limits and Derivatives

Solution:

Apply L'Hopital Rule
$\displaystyle\lim _{x \rightarrow 2}\left(\frac{2 x f(2)-4 f'(x)}{1}\right)$
$=\frac{4(4)-4}{1}=12$