Find where the expression is undefined.

The vertical asymptotes occur at areas of infinite discontinuity.

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).

Find and .

Since , there is no horizontal asymptote.

No Horizontal Asymptotes

No oblique asymptotes are present for logarithmic and trigonometric functions.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

No Horizontal Asymptotes

Find the Asymptotes f(x)=1/( natural log of 1+1/x)-x