# Limit of a function

1. Sep 17, 2012

### hopelesss

1. The problem statement, all variables and given/known data
Hey guys
im trying to figure out what lim x->1 ((x^3)-3x+2) / x-1 is.
I get -1/0 and then when i try factor it i cant get it right..

2. Relevant equations

?

3. The attempt at a solution

lim x->1 x^3-3x+2 / x-1 = lim x->1 1^3-3*1+2 / 1-1 = -1/0

2. Sep 17, 2012

### Staff: Mentor

x3 -3x + 2 is divisible by x - 1. Do you know how to do polynomial long division. If not, there's an article on this technique on wikipedia.
When you write expressions like the above, put parentheses around the entire numerator and the entire denominator, like so:
(x3 - 3x + 2)/(x - 1)

Without them, what you wrote is x3 - 3x + (2/x) - 1.

3. Sep 18, 2012

### hopelesss

I do know abit polynomial division, but i cant see my teacher using this method.
I did mean (x3 - 3x + 2)/(x - 1).

Im used to doing it like this
lim x-> 3 (x-3) / (x3 -9) = lim -> 3 (x-3) / ((x-3)(x+3)) = 1/(3+3) = 1/6
But when i try do this i cant get it right, and i cant cancel the things i dont want 2 have.

4. Sep 18, 2012

### clamtrox

Okay, here's an alternative approach: do you remember that you can write a polynomial into a product form like this
$$p(x) = x^3 + a_2 x^2 + a_1 x + a_0 = (x-r_1)(x-r_2)(x-r_3)$$
where r are the roots of the polynomial?

Now you already noticed that one of the roots is +1. Just write out the right hand side and make all of the coefficients equal. You'll get some equations for the remaining roots, and they should be easy to solve.

5. Sep 18, 2012

### Staff: Mentor

You're the one working this problem, not your teacher. Besides, you are probably underestimating your teacher's abilities. If you know about polynomial long division, why not use it? (x3 - 3x + 2) factors nicely.

6. Sep 18, 2012

### mtayab1994

Use x-1 as a factor in the numerator and then cancel it out with the x-1 in the denominator. BTW if you want to factor with x-1 you'll have to do something called synthetic division.

7. Sep 18, 2012

### vela

Staff Emeritus
You do realize that $1^3-3\times 1 + 2$ is equal to 0, not -1, right?

8. Sep 19, 2012

### hopelesss

HAHAHAHA :D no clue what ive been doing. thx!