Question

The limit of x/|x| as x approaches 0 from the left is -1.

Why is that so? Why is the answer not undefined?

Answer 1

because this function is a constant of \(x<0\) then \(|x|=-x\) and so \(\frac{x}{|x|}=\frac{x}{-x}=-1\)

Answer 2

*if, not "of"

Answer 3

while it is true that it is undefined if \(x=0\) you are asked for a limit, not the actual value of the function at that point. that is the distinction between limits and values of the function

Answer 4

But the limit of x/|x| as x approaches 5 = 1. Why is it that sometimes you can just find the value and that is also the limit.