Question

Find $\underset{h\to 0}{lim}\frac{(a+h{)}^{2}sin(a+h)-a^{2}sina}{h}$

Answer 1

$\underset{h\to 0}{lim}\frac{(a+h{)}^{2}sin(a+h)-a^{2}sina}{h}\underset{h\to 0}{lim}\frac{(a+h{)}^{2}sin(a+h)-a^{2}sina}{h}\underset{h\to 0}{lim}\frac{(a^2+2ah+h^2)sin(a+h)-a^{2}sina}{h}\underset{h\to 0}{lim}\frac{a^4\left[sin\right(a+h)-sina]+h(2a+h)sin(a+h)}{h}\underset{h\to 0}{lim}[\frac{a^4.4cos(a+\frac{h}{2}.sin\frac{h}{2})}{4\times \frac{h}{2}}+\frac{h(4a+h)sin(a+h)}{h}]=4a^2.cos(a+a).1+(2a+a)4sin(a+a)=4a^2.2cosa+2asina$