Question

Find the limits lim_{xrightarrow0}frac{frac{1}{x-1}+frac{1}{x+1}}{x}

Limits and continuity
ANSWERED
asked 2020-11-07
Find the limits
\(\lim_{x\rightarrow0}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}\)

Answers (1)

2020-11-08
Given that \(\lim_{x\rightarrow0}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}\)
Compute the limit as follows.
\(\lim_{x\rightarrow0}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}=\lim_{x\rightarrow0}\frac{x+1+x-1}{x(x-1)(x+1)}\)
\(=\lim_{x\rightarrow0}\frac{2x}{x(x^2-1)}\)
\(=\lim_{x\rightarrow0}\frac{2}{(x^2-1)}\)
\(=\frac{2}{0-1}\)
\(=-2\)
Thus, \(\lim_{x\rightarrow0}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}=-2\)
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