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# Trigonometry Examples

Find where the expression is undefined.

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

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

Simplify the expression.

Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

Cancel the common factor of .

Cancel the common factor.

Divide by .

The oblique asymptote is the polynomial portion of the long division result.

This is the set of all asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

Oblique Asymptotes: