Enter a problem...
Calculus Examples
Step 1
Find where the expression is undefined.
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Step 2
The vertical asymptotes occur at areas of infinite discontinuity.
No Vertical Asymptotes
Step 3
Step 3.1
Divide the numerator and denominator by the highest power of in the denominator, which is .
Step 3.2
Evaluate the limit.
Step 3.2.1
Cancel the common factor of .
Step 3.2.2
Cancel the common factor of .
Step 3.2.2.1
Cancel the common factor.
Step 3.2.2.2
Rewrite the expression.
Step 3.2.3
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 3.2.4
Evaluate the limit of which is constant as approaches .
Step 3.2.5
Move the limit under the radical sign.
Step 3.2.6
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 3.2.7
Evaluate the limit of which is constant as approaches .
Step 3.3
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Step 3.4
Simplify the answer.
Step 3.4.1
Simplify the denominator.
Step 3.4.1.1
Add and .
Step 3.4.1.2
Any root of is .
Step 3.4.2
Divide by .
Step 4
Step 4.1
Divide the numerator and denominator by the highest power of in the denominator, which is .
Step 4.2
Evaluate the limit.
Step 4.2.1
Cancel the common factor of .
Step 4.2.2
Cancel the common factor of .
Step 4.2.2.1
Cancel the common factor.
Step 4.2.2.2
Rewrite the expression.
Step 4.2.3
Split the limit using the Limits Quotient Rule on the limit as approaches .
Step 4.2.4
Evaluate the limit of which is constant as approaches .
Step 4.2.5
Move the term outside of the limit because it is constant with respect to .
Step 4.2.6
Move the limit under the radical sign.
Step 4.2.7
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 4.2.8
Evaluate the limit of which is constant as approaches .
Step 4.3
Since its numerator approaches a real number while its denominator is unbounded, the fraction approaches .
Step 4.4
Simplify the answer.
Step 4.4.1
Cancel the common factor of and .
Step 4.4.1.1
Rewrite as .
Step 4.4.1.2
Move the negative in front of the fraction.
Step 4.4.2
Simplify the denominator.
Step 4.4.2.1
Add and .
Step 4.4.2.2
Any root of is .
Step 4.4.3
Cancel the common factor of .
Step 4.4.3.1
Cancel the common factor.
Step 4.4.3.2
Rewrite the expression.
Step 4.4.4
Multiply by .
Step 5
List the horizontal asymptotes:
Step 6
Use polynomial division to find the oblique asymptotes. Because this expression contains a radical, polynomial division cannot be performed.
Cannot Find Oblique Asymptotes
Step 7
This is the set of all asymptotes.
No Vertical Asymptotes
Horizontal Asymptotes:
Cannot Find Oblique Asymptotes
Step 8