Let f(x) be a differentiable function and f^{ | vedclass

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(D) Given,$f^{\prime}(4)=5$.We need to evaluate the limit $L = \lim _{x \rightarrow 2} \frac{f(4)-f\left(x^{2}\right)}{x-2}$.Since the limit is in the

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-$20$

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(D) Given,$f^{\prime}(4)=5$.We need to evaluate the limit $L = \lim _{x \rightarrow 2} \frac{f(4)-f\left(x^{2}\right)}{x-2}$.Since the limit is in the $\frac{0}{0}$ form,we apply $L$'$H$ôpital's rule by differentiating the numerator and the denominator with respect to $x$.$L = \lim _{x \rightarrow 2} \frac{\frac{d}{dx}[f(4)-f(x^2)]}{\frac{d}{dx}[x-2]}$$L = \lim _{x \rightarrow 2} \frac{0 - f^{\prime}(x^2) \cdot 2x}{1}$Substituting $x=2$,we get:$L = -f^{\prime}(2^2) \cdot 2(2) = -f^{\prime}(4) \cdot 4$Since $f^{\prime}(4)=5$,we have $L = -(5) \cdot 4 = -20$.

Let $f(x)$ be a differentiable function and $f^{\prime}(4)=5$. Then,$\lim _{x \rightarrow 2} \frac{f(4) - f\left(x^{2}\right)}{x-2}$ equals

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