Explanation

(d)
$\lim_{h \rightarrow 0}\frac{f\left( 2h + 2 + h^{2} \right) - f(2)}{f\left( h - h^{2} + 1 \right) - f(1)}$
$= \lim_{h \rightarrow 0}\frac{\left\{ f'\left( 2h + 2 + h^{2} \right) \right\}.(2 + 2h) - 0}{\left\{ f^{'}\left( h - h^{2} + 1 \right) \right\}.(1 - 2h) - 0}$
[using L’ Hospital’s rule]
$= \frac{f^{'}(2).2}{f^{'}(1).1} = \frac{6.2}{4.1} = 3$