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$
- C0
- Ddoes 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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