Limit of a function

  • Thread starter hopelesss
  • Start date
  • #1
hopelesss
15
0

Homework Statement


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..

Homework Equations



?

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
 

Answers and Replies

  • #2
36,307
8,280

Homework Statement


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..
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.

Homework Equations



?

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

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
hopelesss
15
0
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
clamtrox
938
9
Okay, here's an alternative approach: do you remember that you can write a polynomial into a product form like this
[tex] p(x) = x^3 + a_2 x^2 + a_1 x + a_0 = (x-r_1)(x-r_2)(x-r_3) [/tex]
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
36,307
8,280
I do know abit polynomial division, but i cant see my teacher using this method.
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.
I did mean (x3 - 3x + 2)/(x - 1).
 
  • #6
mtayab1994
584
0
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
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
15,563
2,203
lim x->1 1^3-3*1+2 / 1-1 = -1/0
You do realize that ##1^3-3\times 1 + 2## is equal to 0, not -1, right?
 
  • #8
hopelesss
15
0
You do realize that ##1^3-3\times 1 + 2## is equal to 0, not -1, right?

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

Suggested for: Limit of a function

  • Last Post
Replies
6
Views
900
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
1
Views
881
  • Last Post
Replies
7
Views
2K
Top