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How do I solve [math]\lim_{x\rightarrow 0}\left | \frac{x+1}{x-1} \right |[/math]
Okay, how do we do that?
When x approaches 0 from the left, the numerator (x+1) approaches 1, while the denominator (x-1) approaches -1. So we get a limit of [math]\lim_{x\rightarrow 0^-}\left | \frac{x+1}{x-1} \right |[/math] = [math]\lim_{x\rightarrow 0^-} \frac{1-x}{1-x}[/math] = 1.