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Trigonometry Examples
Step 1
Find where the expression is undefined.
Step 2
The vertical asymptotes occur at areas of infinite discontinuity.
No Vertical Asymptotes
Step 3
Step 3.1
Evaluate the limit.
Step 3.1.1
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 3.1.2
Move the term outside of the limit because it is constant with respect to .
Step 3.2
Since the exponent approaches , the quantity approaches .
Step 3.3
Evaluate the limit.
Step 3.3.1
Evaluate the limit of which is constant as approaches .
Step 3.3.2
Simplify the answer.
Step 3.3.2.1
Multiply by .
Step 3.3.2.2
Add and .
Step 4
List the horizontal asymptotes:
Step 5
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 6
This is the set of all asymptotes.
No Vertical Asymptotes
Horizontal Asymptotes:
No Oblique Asymptotes
Step 7