# Thread: Proving infinate limits help!!

1. ## Proving infinate limits help!!

I need to prove that as x-> + infinity, (x+1)/(x-1)= 1

With epsilon delta definitions... this is so confusing, can anyone help?

2. Originally Posted by squintz123
I need to prove that as x-> + infinity, (x+1)/(x-1)= 1

With epsilon delta definitions... this is so confusing, can anyone help?
$\displaystyle \frac{x+1}{x-1} = \frac{x(1+\frac{1}{x})}{x(1-\frac{1}{x})}$

$\displaystyle = \frac{1+\frac{1}{x}}{1-\frac{1}{x}}$

What happens to the two fractions when x tends towards infinity?

EDIT: Ah sorry, I didn't read your need for epsilon delta definitions.

3. Originally Posted by squintz123
I need to prove that as x-> + infinity, (x+1)/(x-1)= 1

With epsilon delta definitions... this is so confusing, can anyone help?
What you want to show is that for any $\displaystyle \epsilon > 0$ there is an $\displaystyle N > 0$ such that

$\displaystyle \left| \frac{x+1}{x-1} - 1\right| < \epsilon$ when $\displaystyle x > N$

$\displaystyle \left| \frac{x+1}{x-1} - 1\right| < \epsilon$
$\displaystyle \left| \frac{2}{x-1}\right| < \epsilon$

$\displaystyle \left| \frac{x-1}{2} \right| > \frac{1}{\epsilon}$
$\displaystyle \left| x - 1\right| > \frac{2}{\epsilon}$
or
$\displaystyle x-1 >\frac{2}{\epsilon}$ (x is very large)

or

$\displaystyle x > \frac{2}{\epsilon} + 1$

This is your N, i.e. $\displaystyle N = \frac{2}{\epsilon} + 1$

Then work the steps in reverse.

4. Thank you so much man. That makes a lot more sense... My professor makes it sound so confusing...