Linear oblique asymptote

  • Thread starter Coco12
  • Start date
  • #1
Coco12
272
0

Homework Statement



what is the linear oblique asymptote of (x^5+x^3+2)/(x^4-1)
?

Homework Equations



x-a/p(x) = q(x) +remainder

The Attempt at a Solution



I put in all the placeholders for the divisor and the numerator and got x as the equation for the linear oblique asymptote?? Is that right??
 

Answers and Replies

  • #2
Mentallic
Homework Helper
3,802
94
We would let

[tex]\frac{x^5+x^3+2}{x^4-1}\equiv \frac{(ax+b)(x^4-1)+p(x)}{x^4-1} = ax+b + \frac{p(x)}{x^4-1}[/tex]

Where p(x) is a cubic polynomial or less (doesn't matter what it is exactly).


If we expanded (ax+b)(x4-1) then we get

[tex]ax^5+bx^4-ax-b[/tex]

But we ignore the -ax-b term because that will be a part of p(x) which we've already said we don't care about. So we want the constant a to be chosen such that [itex]ax^5=x^5[/itex] since the coefficient of [itex]x^5[/itex] on the LHS must be equal to the RHS, hence a=1, and b must be chosen such that [itex]bx^4=0[/itex] for the same reason, hence b=0.

But we ignore the -ax-b term because that will be a part of p(x) which we've already said we don't care about.
 
  • #3
Coco12
272
0
Is the answer that I got correct? Thanks for taking the time to answer. I know how to do it just wondering if it's correct
 

Attachments

  • image.jpg
    image.jpg
    2.1 KB · Views: 333
  • #4
HallsofIvy
Science Advisor
Homework Helper
43,021
970
Yes, y= x is the "liner oblique asymptote".
 
  • #5
36,310
8,280
Is the answer that I got correct? Thanks for taking the time to answer. I know how to do it just wondering if it's correct
No, this isn't correct. It's the equation of the rational function you started with.

To find the oblique asymptote, either do what Mentallic suggested or carry out the long division to get x + a proper rational function. In a proper rational function, the degree of the numerator is less than that of the denominator.
 
  • #6
Coco12
272
0

Suggested for: Linear oblique asymptote

  • Last Post
Replies
3
Views
5K
Replies
1
Views
1K
Replies
3
Views
3K
  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
14
Views
3K
  • Last Post
Replies
6
Views
7K
  • Last Post
Replies
6
Views
11K
Top