Calculus Examples

Find the Asymptotes y=x+ natural log of |x|
Step 1
Find where the expression is undefined.
Step 2
Ignoring the logarithm, 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 3
There are no horizontal asymptotes because is .
No Horizontal Asymptotes
Step 4
No oblique asymptotes are present for logarithmic and trigonometric functions.
No Oblique Asymptotes
Step 5
This is the set of all asymptotes.
Vertical Asymptotes:
No Horizontal Asymptotes
Step 6