DerivativeApplications

# 6. 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 the function:

Solutions: x = 1/2; y = x + 1/2

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