 # Determine the following limits. lim_{xrightarrow1}frac{1-x^2}{(x-1)^2} generals336 2021-03-02 Answered
Determine the following limits.
$\underset{x\to 1}{lim}\frac{1-{x}^{2}}{\left(x-1{\right)}^{2}}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it saiyansruleA

Given information:
$\underset{x\to 1}{lim}\frac{1-{x}^{2}}{\left(x-1{\right)}^{2}}$
To determine the limits first simplify,
$\underset{x\to 1}{lim}\frac{1-{x}^{2}}{\left(x-1{\right)}^{2}}=\underset{x\to 1}{lim}\left(\frac{\left(1-x\right)\left(1+x\right)}{\left(x-1{\right)}^{2}}\right)$
$=\underset{x\to 1}{lim}\left(\frac{\left(1+x\right)}{\left(x-1\right)}\right)$
$=\underset{x\to 1}{lim}\left(1+x\right)\cdot \underset{x\to 1}{lim}\left(\frac{1}{\left(x-1\right)}\right)$
$=\left(1+1\right)\cdot \left(\frac{1}{1-1}\right)$
$=2\left(\frac{1}{0}\right)$
$=\mathrm{\infty }$

###### Not exactly what you’re looking for? Jeffrey Jordon