Determine the following limits. lim_{xrightarrow1}frac{1-x^2}{(x-1)^2}

Determine the following limits. lim_{xrightarrow1}frac{1-x^2}{(x-1)^2}

Question
Limits and continuity
asked 2021-03-02
Determine the following limits.
\(\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}\)

Answers (1)

2021-03-03
Given information:
\(\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}\)
To determine the limits first simplify,
\(\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}=\lim_{x\rightarrow1}(\frac{(1-x)(1+x)}{(x-1)^2}\)
\(=\lim_{x\rightarrow1}(\frac{(1+x)}{(x-1)})\)
\(=\lim_{x\rightarrow1}(1+x)\cdot\lim_{x\rightarrow1}(\frac{1}{(x-1)})\)
\(=(1+1)\cdot(\frac{1}{1-1})\)
\(=2(\frac{1}{0})\)
\(=\infty\)
0

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