In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. In some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity. There are two types of asymptote: one is horizontal and other is vertical. Also, a special type of asymptote exists that is an oblique asymptote. Below mentioned are the asymptote formulas.
This can be shown graphically as:
Solved Example
Question 1: Find the asymptotes for
We can see at once that there are no vertical asymptotes as the denominator can never be zero.
Thus, this refers to the vertical asymptotes.
Now see what happens as x gets infinitely large:
The method we have used before to solve this type of problem is to divide through by the highest power of x.
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This is the horizontal asymptotes of the give function.
| More topics in Asymptote Formula | |
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