Evaluate the following limit : lim(h→0) ((a + h)^2 sin (a + h) - a^2 sin a)/h

Question

Evaluate the following limit : \(\lim\limits_{h \to0} \cfrac{(a+h)^2\,sin(a+h)-a^2\,sin\,a}h\)

lim(h→0) ((a + h)² sin (a + h) - a² sin a)/h

Answer 1

To find: \(\lim\limits_{h \to0} \cfrac{(a+h)^2\,sin(a+h)-a^2\,sin\,a}h\)

We know,

(a + b)² = a² + b² + 2ab

Therefore,

Now,

We get,

Formula used:

= a² cos a + 2a sin a

Hence, the value of

\(\lim\limits_{h \to0} \cfrac{(a+h)^2\,sin(a+h)-a^2\,sin\,a}h\) 

= a² cos a + 2a sin a