Question

The value of $\underset{h\to 0}{lim}\frac{(a+h{)}^2\sin (a+h)-a^2\sin a}{h}$ is

• A. $2a\sin a+a^2\cos a$
• B. $2a\sin a-a^2\cos a$
• C. $2a\cos a+a^2\sin a$
• D. none of these

Answer 1

Answer: (A)

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

Using L Hospital's rule,

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

$=\underset{h\to 0}{lim}\frac{(a+h{)}^2\cos (a+h)+\sin (a+h\left).2\right(a+h)}{1}$

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