Question

find the limit as x approaches positive two 1/x-2

Answer 1

Well, as x approaches 2, the bottom approaches 0 so it gets really really small. Then 1 over that must be approaching what?

Answer 2

one?

Answer 3

Nope. Look at it this way.
1/1 = 1
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
1/0.0001 = 10000
so you can see that if we have 1 over something that is getting smaller and smaller, then the whole thing is getting bigger and bigger.

Answer 4

so its approaching infinity

Answer 5

Exactly :)

Answer 6

but what if the positive two were negative....would it be approaching negative infinity

Answer 7

Positive two itself cannot be negative ;)
But I believe what you mean is, "if x approached 2 from the negative side". Then the bottom would always be negative, so indeed the fraction would approach negative infinity. If however, x approached from the other side, the fraction would approach positive infinity.