Thread: Limit question

What is the limit of (|x|)/x? I know from looking at the graph that it has to be 0, but i dont know how to do this algebraically. Thanks.

Originally Posted by Evan.Kimia

What is the limit of (|x|)/x? I know from looking at the graph that it has to be 0, but i dont know how to do this algebraically. Thanks.

as x--> what?
if x-->0
You are supposed to consider the limit as x-->0 from right and from left.

at x>0 |x|/x =1
therefor limit at x>0 is 1
at x<0 |x|/x=-1
therfor limit at x<0 is -1
1 and -1 are the right hand limit and left hand limit at x=0 respectively.
since they are not equal therefor at x=0 limit don't exist.

Originally Posted by nikhil

at x>0 |x|/x =1
therefor limit at x>0 is 1
at x<0 |x|/x=-1
therfor limit at x<0 is -1
1 and -1 are the right hand limit and left hand limit at x=0 respectively.
since they are not equal therefor at x=0 limit don't exist.

Edit:
limit when
limit when

Originally Posted by General

Edit:
limit when
limit when

x>0 may take any value not only 0+ebsilon but also real number
eg
limit of |x|/x at x>0 (let us take x=5)
=|5|/5 =1

Thank you! Refreshed my memory.