2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Functions

JEE Main & Advanced Mathematics Functions Question Bank Limits

  • question_answer
    The value of the limit of \[\frac{{{x}^{3}}-8}{{{x}^{2}}-4}\]as x tends to 2 is [SCRA 1996]

    A)                 3

    B)                 \[\frac{3}{2}\]

    C)                 1

    D)                 0

    Correct Answer: A

    Solution :

                       \[\underset{x\to 2}{\mathop{\lim }}\,\,\,\frac{{{x}^{3}}-8}{{{x}^{2}}-4}\],          \[\left( \frac{0}{0}\,\text{form} \right)\]            Applying L-Hospital's rule, we get                                 \[\underset{x\to 2}{\mathop{\lim }}\,\,\,\frac{3{{x}^{2}}}{2x}=\underset{x\to 2}{\mathop{\lim }}\,\,\,\frac{3\times 2\times 2}{2\times 2}=3\].


You need to login to perform this action.
You will be redirected in 3 sec spinner