How do you find the limit of $|x|/x$ as x approaches $0$ ?

Question

138972 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-26T11:11:24

Does not exist

For $x < 0$ , $(abs x)/x = (-x)/x = -1$

For $x >0$ , $(abs x)/x = x/x = 1$

Thus
$lim_(x to 0^-) abs x/x = -1$

$lim_(x to 0^+) abs x/x = 1$

So the limit does not exist.

graph{|x|/x [-10, 10, -5, 5]}

How do you find the limit of |x|/x |x|/x as x approaches 00?