$\underset{h→0}{\lim}\frac{(a+h)^2\sin (a+h)-a^2\sin a}{h}$ is equal to

$a\cos a+a^2\sin a$ $a\sin a+a^2\cos a$ $2a\sin a+a^2\cos a$ $2a\cos a+a^2\sin a$

$2a\sin a+a^2\cos a$

$\underset{h→0}{\lim}\frac{(a+h)^2\sin (a+h)-a^2\sin a}{h}$   Apply L’Hospital’s rule $\underset{h→0}{\lim}\frac{2(a+h)\sin (a+h)+(a+h)^2\cos (a+h)}{1}=2a\sin a+a^2\cos a$