Question

lim X approach to zero..limx​

Answer 1

Answer:

In order for the limit to exist, you need the side limits to commute. In this case :

limx→0|x|=limx→0|x|={limx→0+x, x≥0limx→0−−x, x<0={0, x≥00, x<0

which means that the side limits are equal and thus : limx→0|x|=0.

As far as the |x|x part, if you divide something by a quantity, you will also need to multiply it by that. This is why you're getting 1 as a wrong answer there.