Question

can someone explain to me why the limit as x approaches 2 of 1/(x-2)^2 is infinite?

Answer 1

Take 2.0000001 as a value of x
If you subtract 2 from this value, you'll get something which is incredibly close to 0
This value, if squared, becomes even smaller
When a number is divided by an extremely small number, it becomes bigger, as on 2/0.1=20.
Now I think you get it. :D

Answer 2

You can also see that there is a vertical asymptote at x=2. (Set denominator equal to 0)
So, as x approaches 2, the graph goes to infinity.

Answer 3

oh i see thank you guys i understand now!:)