What is lim ([|x|] - x)/(3-x) as x approaches 3 from the left? Please include the process of solving. Thank you.

Question

It is one of the items in my problem set. 

I am enroled at a distance learning program and I see my professor rarely. I hope someone could help.

Answer 1

When x>0, |x|=x

 

As x->3 from the left, x>0 and (|x|-x)=(x-x)=0 throughout.

 

(3-x)>0 as x->3 from the left.

 

Therefore (|x|-x)/(3-x) is zero throughout.

 

The limit is 0.