Confused About Limit x->0- |x|: Seeking Explanation

[khurram usman]

Homework Statement

the answer to this question [limit x->0- |x|] given to me by my instructor was -1. (by 0- i mean to say the left handed limit). i have been thinking for the last 15 minutes but could not understand it.

i think the answer should be 0 because as we get closer to zero from the left side the distance between 0 and our number gets smaller and smaller till finally it approaches 0 itself.

and as for the right hand limit of same question ( limit x->0+ |x|) i was given the answer 0 and that seems corret to me.
so anyone please explain this..
thanks

 

[Hootenanny]

Homework Statement

the answer to this question [limit x->0- |x|] given to me by my instructor was -1. (by 0- i mean to say the left handed limit). i have been thinking for the last 15 minutes but could not understand it.

i think the answer should be 0 because as we get closer to zero from the left side the distance between 0 and our number gets smaller and smaller till finally it approaches 0 itself.

and as for the right hand limit of same question ( limit x->0+ |x|) i was given the answer 0 and that seems corret to me.
so anyone please explain this..
thanks

You are correct, the limit of |x| as x $\to$ 0 exists and is 0.

$$\lim_{x\to0^-} |x| = \lim_{x\to0^+} |x| = \lim_{x\to0} |x| = 0$$

Perhaps it was a typo in your instructor's answer.

 

[HallsofIvy]

Or perhaps the problem was intended to be
$$\lim_{x\to 0^-} \frac{|x|}{x}$$

 

[stallionx]

Homework Statement

the answer to this question [limit x->0- |x|] given to me by my instructor was -1. (by 0- i mean to say the left handed limit). i have been thinking for the last 15 minutes but could not understand it.

i think the answer should be 0 because as we get closer to zero from the left side the distance between 0 and our number gets smaller and smaller till finally it approaches 0 itself.

and as for the right hand limit of same question ( limit x->0+ |x|) i was given the answer 0 and that seems corret to me.
so anyone please explain this..
thanks

Since you're approaching from the left what you're dealing with is a negative number and absolute value goes out as ( - x ) but x=0 so - x = - 0 = Zero