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.

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!

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