_ x a 1 (x-a)^ 2n-1 (n N) equals: - Vidyadip

MCQ

$\lim_\limits{\text{x} \rightarrow \text{a}}\frac{1}{(\text{x}-\text{a})^{2\text{n}-1}}(n\ \epsilon\ N)$ equals:

A
$ \infty$
B
$ -\infty$
C
$0$
✓
does not exist

✓

Answer

Correct option: D.

does not exist

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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