# Easy limit problem

1. Feb 25, 2008

### tony873004

$$\mathop {\lim }\limits_{t \to 1} \,\frac{{t - 1}}{{t^2 - 1}}$$

I thought we were taught to simply divide the coefficients of the highest term, in this case, 0t2 for the numerator and 1 t2 for the denominator. 0/1=0. But I know the limit is 0.5 from substituting 0.9999999999 for t in my calculator.

I must be getting this "coefficient of highest term" method mixed up with something else. Why doesn't it work here?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 25, 2008

### sutupidmath

well what u need to do is
$$t^{2}-1=(t-1)(t+1)$$
can u go from here?
This is just the difference of squares. Its general form is:

$$a^{2}-b^{2}=(a-b)(a+b)$$

Last edited: Feb 25, 2008
3. Feb 25, 2008

### HallsofIvy

Staff Emeritus
I strongly suspect you were taught that for limits as t goes to infinity! That is not the problem here.

4. Feb 26, 2008

### tony873004

Thanks for the explanation, sutupid.

You're probably right, Halls. I'll never forget this now. This was part of a larger problem in Calc III. That's the problem with Calc III. Every now and then they assume you remember your Calc I :)

5. Feb 26, 2008

### sutupidmath

Honestly, this had almost nothing to do with calc I, it was just a simple algebra trick!

6. Feb 26, 2008

### HallsofIvy

Staff Emeritus
Well, the tiny part about finding the limit might be from calculus I!
(And you did say "almost nothing".)

7. Feb 26, 2008

### tony873004

Algebra class was 20 years ago for me. Everything I currently know about Algebra I learned in Calc I.