question_answer

It is given that f'(a) exists, then \[\underset{x\to a}{\mathop{\lim }}\,\,\,\frac{x.f(a)-a.f(x)}{x-a}\] is equal to

A)  \[f\,\left( a \right)+a\,f'\left( a \right)\]       

B)  \[f\left( a \right)a\text{ }f\left( a \right)\]

C)  \[f\left( a \right)\]                       

D)  \[-\text{ }f'\left( a \right)\]

E)  None of these