how to take limit as x-->0+ of x/abs x? and as x-->0-?

Question

step by step plz

Answer 1

Hi,

limit as x-->0+ of x/abs x = 1
limit as x-->0- of x/abs x = -1

Look at the graph of y = x/|x| to see this.
I hope that helps!! :-)

Answer 2

When x >0, the function equals the constant function 1.

When x < 0, the function equals the constant function -1.

And both of those have pretty obvious limits. ;)

It's really that simple.