# Calculus Examples

Step 1
Find where the expression is undefined.
Step 2
Since as from the left and as from the right, then is a vertical asymptote.
Step 3
Since as from the left and as from the right, then is a vertical asymptote.
Step 4
List all of the vertical asymptotes:
Step 5
Consider the rational function where is the degree of the numerator and is the degree of the denominator.
1. If , then the x-axis, , is the horizontal asymptote.
2. If , then the horizontal asymptote is the line .
3. If , then there is no horizontal asymptote (there is an oblique asymptote).
Step 6
Find and .
Step 7
Since , the x-axis, , is the horizontal asymptote.
Step 8
There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.
No Oblique Asymptotes
Step 9
This is the set of all asymptotes.
Vertical Asymptotes:
Horizontal Asymptotes:
No Oblique Asymptotes
Step 10