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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{{{\left( \int\limits_{0}^{x}{{{e}^{{{t}^{2}}}}dt} \right)}^{2}}}{\int\limits_{0}^{x}{{{e}^{2{{t}^{2}}}}dt}}\]is equal to

    A)  0                                            

    B)  e

    C) \[{{e}^{2}}\]                                      

    D)  1

    Correct Answer: A

    Solution :

    \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{2{{\left( \int\limits_{0}^{x}{{{e}^{{{t}^{2}}}}dt} \right)}^{2}}.{{e}^{{{x}^{2}}}}}{{{e}^{2{{x}^{2}}}}}\] \[\underset{x\to \infty }{\mathop{\text{L}im}}\,\frac{2\int\limits_{0}^{x}{{{e}^{{{t}^{2}}}}dt}}{{{e}^{{{x}^{2}}}}}=\underset{x\to \infty }{\mathop{\text{L}im}}\,\frac{2{{e}^{{{x}^{2}}}}}{2x{{e}^{{{x}^{2}}}}}=0\]


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