Answer to Question #2205 in Calculus for lalu

Question

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

Answer 1

<img src="/cgi-bin/mimetex.cgi?%5Clim_%7Bx%20%5Cto%201%7D%20%5Cfrac%7B1%7D%7B1-x%7D-%5Cfrac%7B1%7D%7B1-x%5E2%7D%20=%20%5Clim_%7Bx%20%5Cto%201%7D%20%5Cfrac%7B%281+x-1%29%7D%7B%281-x%29%281+x%29%7D%20=%20%5Clim_%7Bx%20%5Cto%201%7D%20%5Cfrac%7Bx%7D%7B1-x%5E2%7D%20=%20%5Cfrac%7B1%7D%7B0%7D%20=%20%5Cinfty" title="\lim_{x \to 1} \frac{1}{1-x}-\frac{1}{1-x^2} = \lim_{x \to 1} \frac{(1+x-1)}{(1-x)(1+x)} = \lim_{x \to 1} \frac{x}{1-x^2} = \frac{1}{0} = \infty">