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Asymptotes

To calculate the asymptotes we have to calculate these limits:

- Horizontal asymptotes:

- Vertical asymptotes:

- Oblique asymptotes:

NOTE: if you have a rational function,

- You have to look for the vertical asymptotes in the roots of Q(x).


- When deg P < deg Q, there is a horizontal asymptote y = 0


- When deg P = deg Q, there is a horizontal asymptote


- When deg P = deg Q + 1, there is an oblique asymptote


Example1:

Vertical asymptote: x = -2
Oblique asymptote: y = x + 3

Example 2:

Vertical asymptote: x = 0
Horizontal asymptote: y = 0

 

Exercise: find the asymptotes of these functions:

 

 

Solutions: a) y = 1; b) x = 0, y = x