question_answer

If the function f(x) is differentiable at x = a, then \[\underset{x\to a}{\mathop{\lim }}\,\frac{{{x}^{2}}f(a)-{{a}^{2}}f(x)}{x-a}\]  is equal to ________.

A)  \[2a\,\,f\,\,(a)-{{a}^{2}}f'\,\,(a)\]          

B)  \[2a\,\,f\,\,(a)+{{a}^{2}}f'\,\,(a)\]

C)  \[-{{a}^{2}}f'\,\,(a)\]               

D)  \[a\,\,f\,\,(a)-{{a}^{2}}f'\,\,(a)\]

E)  None of these