MCQ
$\lim_\limits{\text{x} \rightarrow \text{a}}​\frac{1}{(\text{x}-\text{a})^{2\text{n}-1}}​(\text{n ϵ N})$ equals:
  • A
    $ \infty$
  • B
    $ -\infty$
  • C
    0
  • D
    does not exist

Answer

  1. does not exist

Solution:

Left hand limit is$\lim_\limits{\text{x} \rightarrow \text{a}}​\frac{1}{(\text{x}-\text{a})^{2\text{n}-1}}​​​​​=-\infty$

And Right hand limit is $\lim_\limits{\text{x} \rightarrow \text{a}}​\frac{1}{(\text{x}-\text{a})^{2\text{n}-1}}​​​​​=+\infty$

$\text{L.H.L.}\neq \text{R.H.L.}$

Therefore, the given limit does not exist.

Hence, the option D is correct.

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