Question

Evaluate lim x ->1(1/(1-x) -1/(1-x[sup]2[/sup]))

Answer 1

<img src="/cgi-bin/mimetex.cgi?\lim_{x \to 1} (\frac{1}{1-x} - \frac{1}{1-x^2}) = \lim_{x \to 1} \frac{1+x -1}{1-x^2}= \\ \lim_{x \to 1} \frac{x}{1-x^2} \to \frac{1}{0}= \infty" title="\lim_{x \to 1} (\frac{1}{1-x} - \frac{1}{1-x^2}) = \lim_{x \to 1} \frac{1+x -1}{1-x^2}= \\ \lim_{x \to 1} \frac{x}{1-x^2} \to \frac{1}{0}= \infty" />