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