A) \[af'\,(a)-f(a)\]
B) \[af\,\,(a)+f'(a)\]
C) \[af'\,(a)+f(a)\]
D) \[af\,(a)-f'(a)\]
Correct Answer: A
Solution :
\[\underset{x\to a}{\mathop{\lim }}\,\frac{af\,(x)-xf(a)}{x-a}\] \[=\underset{x\to a}{\mathop{\lim }}\,\frac{af\,(x)-af(a)+af(a)-xf(a)}{x-a}\] \[\underset{x\to a}{\mathop{\lim }}\,\frac{a[f\,(x)-f(a)]}{x-a}-\underset{x\to a}{\mathop{\lim }}\,\,f(x)\] \[af'\,(a)-f(a)\]
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