A) a
B) a f [a]
C) \[\frac{a}{2}f(a)\]
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to a}{\mathop{\lim }}\,\frac{x\int_{0}^{x}{f(t)dt}}{x-a}\] \[\left( \text{from}\frac{\text{0}}{\text{0}} \right)\] \[=\underset{x\to a}{\mathop{\lim }}\,\left\{ \frac{xf(x)+\int_{0}^{x}{f(t)dt}}{1} \right\}\]\[=\frac{af(a)+0}{1}=af(a)\]You need to login to perform this action.
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