The value of $\lim_{n \rightarrow \infty}\frac{x^{n}}{x^{n} + 1}$, where $x

Question

The value of $\lim_{n \rightarrow \infty}\frac{x^{n}}{x^{n} + 1}$, where $x < - 1$ is

Dr. Abubacker · Accepted Answer

(c)
$\lim_{n \rightarrow \infty}\frac{x^{n}}{x^{n} + 1} = \lim_{n \rightarrow \infty}\frac{x^{n}}{{(1 + 1/x^{n})x}^{n}}$
$= \lim_{n \rightarrow \infty}\frac{1}{1 + \frac{1}{x^{n}}} = 1$

Q. The value of $\lim_{n \rightarrow \infty}\frac{x^{n}}{x^{n} + 1}$, where $x < - 1$ is

Explanation

Reviewed by Dr. Abubacker

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