Problem

Solutions For Calculus Chapter 2.2 Problem 8E

Step-by-Step Solution

Solution 1

Given that \(\lim _{x \rightarrow-1} \frac{x^{2}-1}{x^{2}-2 x+1}\)

$$ \begin{aligned} &\lim _{x \rightarrow-1} \frac{x^{2}-1}{x^{2}-2 x+1}=\lim _{x \rightarrow 1} \frac{(x+1)(x-1)}{(x-1)(x-1)} \\ &=\lim _{x \rightarrow-1} \frac{(x+1)}{(x-1)} \end{aligned} $$

As \(x 1^{+}, f(x)+\)

As \(x 1^{-}, f(x)-\)

Since \(f(x)\) does not approaches a fixed number, so limit does not exist.

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