A) \[a{f}'\,(a)-f\,(a)\]
B) \[af\,(a)-f'(a)\]
C) \[a{f}'\,(a)+f\,(a)\]
D) \[af\,(a)+f'(a)\]
Correct Answer: A
Solution :
\[\underset{x\to a}{\mathop{\lim }}\,\,\frac{af(x)-xf(a)}{x-a}\]Þ \[\underset{x\to a}{\mathop{\lim }}\,\,\frac{af(x)-xf(a)+af(a)-af(a)}{x-a}\] Þ \[\underset{x\to a}{\mathop{\lim }}\,\,\frac{a[f(x)-f(a)]-f(a)[x-a]}{x-a}\] Þ \[\underset{x\to a}{\mathop{\lim }}\,\,\frac{a[f(x)-f(a)]}{x-a}-\underset{x\to a}{\mathop{\lim }}\,\,f(a)\] Þ \[a{f}'(a)-f(a)\].You need to login to perform this action.
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