If f(x) = (x+1)/(x-1), what is:

Question

i) lim f(x) as x approaches 1
ii) lim f(x) as x approaches ∞

My answer:
i) lim f(x) as x approaches 1 is undefined because 2/0 is undefined
ii) lim f(x) as x approaches ∞ = ∞
(∞+1)/( ∞-1) = ∞/∞ = ∞

Answer 1

I agree with your first part, but not the second

get a "feel" for the numbers,
e.g. let x = 1000
then f(1000) = 1001/999 = appr 1.002
let x = 1,000,000
then f(1000000) = 1000001/999999 = 1.000002..

if you take large negative values you will get appr .9999...
So don't you agree that you get 1 ?