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## Homework Statement

Evaluate the limit if it exists

## Homework Equations

[tex]\lim_{x\to 0} \frac{1}{x}-\frac{1}{|x|}[/tex]

## The Attempt at a Solution

1) [tex]\lim_{x\to 0} \frac{1}{x}-\frac{1}{|x|}[/tex]

2a) [tex]\lim_{x\to 0} \frac{1}{x}-\frac{1}{x}[/tex]

2b) [tex]\lim_{x\to 0} \frac{1}{x}-\frac{1}{-x}[/tex]

3a) [tex]\lim_{x\to 0} 0 = 0[/tex]

3b) [tex]\lim_{x\to 0} \frac{1}{2x}[/tex]

4)[tex]\lim_{x\to 0} \frac{1}{2}x[/tex]

5)[tex] (\frac{1}{2})0 = 0[/tex]

Did I do this correctly?

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