Evaluate: `lim_(h->0)((a+h)^2sin(a+h)-a^2sina)/h`

Explanation

`lim_(h->0)((a+h)^2sin(a+h)-a^2sina)/h`


We know,


`lim_(x->0) (sinx)/(x)=1`


`lim_(h->0)((a+h)^3-a^3)/h`


Applying L'Hopital Rule:


`lim_(x rightarrow b) (f(x))/(g(x))=lim_(x rightarrow b) (f'(x))/(g'(x))`


`lim_(h->0)((a+h)^3-a^3)/h=lim_(h->0) (3(a+h)^2)/1`


`lim_(h->0) (3(a+h)^2)`


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