If f is differentiable in (0, 6) and f'(4) = | vedclass

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(D) Let $L = \lim_{x 	o 2} \frac{f(4) - f(x^2)}{2 - x}$.Since the limit is of the form $\frac{0}{0}$ as $x 	o 2$,we apply $L$'$H$ôpital's Rule.Diffe

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$20$

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(D) Let $L = \lim_{x 	o 2} \frac{f(4) - f(x^2)}{2 - x}$.Since the limit is of the form $\frac{0}{0}$ as $x 	o 2$,we apply $L$'$H$ôpital's Rule.Differentiating the numerator and denominator with respect to $x$:$L = \lim_{x 	o 2} \frac{\frac{d}{dx}(f(4) - f(x^2))}{\frac{d}{dx}(2 - x)}$$L = \lim_{x 	o 2} \frac{0 - f'(x^2) \cdot (2x)}{-1}$$L = \lim_{x 	o 2} (2x \cdot f'(x^2))$Substituting $x = 2$:$L = 2(2) \cdot f'(2^2) = 4 \cdot f'(4)$Given $f'(4) = 5$,we have:$L = 4 \cdot 5 = 20$.

If $f$ is differentiable in $(0, 6)$ and $f'(4) = 5$,then $\lim_{x \to 2} \frac{f(4) - f(x^2)}{2 - x} = $

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