Question

What is limit of |x| as it approach zero?

Answer 1

`lim_(xrarr0)|x|=0`

Explanation:

The absolute value function `|x|` can be expressed as the piecewise function `|x|={[x,x>=0],[-x,x<0]:}`

A function has a limit at a point if the limits to that point from both sides have the same value.

`lim_(xrarr0^+)|x|=lim_(xrarr0^+)x=0`
`lim_(xrarr0^-)|x|=lim_(xrarr0^-)-x=-0=0`

Therefore, `lim_(xrarr0)|x|=0`