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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    Consider the following: 1. \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}\] exists. 2. \[\underset{x\to 0}{\mathop{\lim }}\,\,\,{{e}^{\frac{1}{x}}}\] does not exist. Which of the above is/are correct?

    A) 1 only

    B) 2 only

    C) Both 1 and 2

    D) Neither 1 nor 2

    Correct Answer: B

    Solution :

    [b] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}=\frac{1}{0}=\infty \] which does not exist. Hence, statement-1 is incorrect. Now, \[\underset{x\to 0}{\mathop{\lim }}\,{{e}^{1/x}}={{e}^{\infty }}\] which also does not exist. Hence, statement-2 is correct.


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