Given information:

\(\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}\)

To determine the limits first simplify,

\(\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}=\lim_{x\rightarrow1}(\frac{(1-x)(1+x)}{(x-1)^2}\)

\(=\lim_{x\rightarrow1}(\frac{(1+x)}{(x-1)})\)

\(=\lim_{x\rightarrow1}(1+x)\cdot\lim_{x\rightarrow1}(\frac{1}{(x-1)})\)

\(=(1+1)\cdot(\frac{1}{1-1})\)

\(=2(\frac{1}{0})\)

\(=\infty\)

\(\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}\)

To determine the limits first simplify,

\(\lim_{x\rightarrow1}\frac{1-x^2}{(x-1)^2}=\lim_{x\rightarrow1}(\frac{(1-x)(1+x)}{(x-1)^2}\)

\(=\lim_{x\rightarrow1}(\frac{(1+x)}{(x-1)})\)

\(=\lim_{x\rightarrow1}(1+x)\cdot\lim_{x\rightarrow1}(\frac{1}{(x-1)})\)

\(=(1+1)\cdot(\frac{1}{1-1})\)

\(=2(\frac{1}{0})\)

\(=\infty\)