2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-6

  • question_answer
    Directions: Question No. 95 are based on the following paragraph. If f(x) and g(x) be two function, such that f [a] = g [a] = 0 and f and g are both differentiable at everywhere in some neighborhood of point a except possibly a. The \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)}{g(x)}=\underset{x\to a}{\mathop{\lim }}\,\frac{f'(x)}{g'(x)'}\] provided \[f'\,(a)\] and \[g'\,(a)\]are not both zero  The value of \[\underset{x\to a}{\mathop{\lim }}\,\frac{x\int_{a}^{x}{f(t)dt}}{x-a}\] is

    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.
You will be redirected in 3 sec spinner