Vertical,
Horizontal, and Slant Asymptotes – (continued)
|
The line y
= mx
+ b is a slant asymptote of the curve
y = f(x) provided that either lim
[f(x) – (mx + b)]
= 0 x→ +∞ or lim [f(x)
– (mx + b)]
= 0 x→˗ ∞ |
|
Slant asymptotes may occur
when you have a ratio of polynomials.
i.e. Suppose f(x)
= p(x)/q(x) where p(x) is 1 degree larger than q(x). Then long division yields: f(x) = mx + b + g(x) where m ≠ 0 and if
lim
g(x) =
0 y
= f(x) = mx + b is a slant asymptote. x→ ± ∞ |
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