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# 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,
$$\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}=\lim_{x\rightarrow1}(\frac{(1-x)(1+x)}{(x-1)^2}$$
$$=\lim_{x\rightarrow1}(\frac{(1+x)}{(x-1)})$$
$$=\lim_{x\rightarrow1}(1+x)\cdot\lim_{x\rightarrow1}(\frac{1}{(x-1)})$$
$$=(1+1)\cdot(\frac{1}{1-1})$$
$$=2(\frac{1}{0})$$
$$=\infty$$

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