Another riddle (Help Eibroaaar)

[Eibro]

lim x->0- ( ( 1 / x ) - ( 1 / |x| ) )
I think it should be -infinity, since we have 1 / (a very large negative number) - 1 / ( a very large positive number ) yet my calculus book lists it as 0. Help!

Mr. Calculus professor told us 1 / |x| could be evaluated to 1 / -x in the case where x -> 0-. That is how I deduced the above.

[Yoni]

x -> 0-, therefore x is always negative.

1/x is a negative numer.
1/|x| is a positive number.

Hence 1/x - 1/|x| is equal to 2/x, or a negative number that approaches -infinity.

A miscommunication is between:
1. You and the book
2. You and the teacher
3. The book and the teacher
4. You and this forum

Discover who is wrong and post back with more!

[Eibro]

Oops. You're right. The calculus book lists it as undefined. So negative infinity seems to be the answer.