Epsilon Delta Proof with Infinity
I have a question about an Epsilon Delta proof in the form of f(x) = L, where x goes to infinity and L is 1/3.
(x^2 + x - 1) / (3*x^2 - 1) = 1/3 (where x goes to infinity)
For the question I did the following things:
I wrote the whole expression (A) in the following way:
A - (1/3) < Epsilon
The function did not get simplified nicely at the end, and I had to to use the square root formula to get x at the end:
I got this as inequality for x:
x > (1 + sqrt(1 - 8Epsilon + 12Epsilon^2)) / 6Epsilon
From that point I didn't know how to continue. I will be more than glad, if you could give me an idea.