how do you find the oblique asymptote?

ex. q(x) = x^5/ (x^3 - 125)

I think I remember that to get oblique or slant asymptotes, the numerator has to be one degree larger than the denominator, and in this, it is two degrees.

so if the numerator is one degree higher than how would you find the oblique asymptote?

such as
q(x) = (x^2 + x - 9)/(2 x - 4)

divide the numberator by the denominator. You will get a first degree equation + remainder. The first degree equation is the slant asymtote.

http://www.purplemath.com/modules/asymtote3.htm

okay thank you.

To find the oblique asymptote, we need to determine the behavior of the function as it approaches infinity or negative infinity.

Here's how you can find the oblique asymptote for the given equation q(x) = x^5 / (x^3 - 125):

1. Divide the numerator by the denominator to obtain a quotient. In this case, divide x^5 by x^3 - 125.

q(x) = x^5 / (x^3 - 125)

2. Simplify the expression if possible. In this case, it cannot be simplified further.

3. Analyze the degree of the quotient's numerator and denominator. In this case, the numerator has a degree of 5, and the denominator has a degree of 3.

4. Determine the difference in degrees. Subtract the degree of the denominator from the degree of the numerator. In this case, 5 - 3 = 2.

5. If the difference in degrees is exactly 1, then there is a slant asymptote. If the difference is greater than 1, then there is no slant asymptote.

In this example, the difference in degrees is 2, which means that there is a slant asymptote.

6. To find the equation of the oblique asymptote, perform long division between the numerator and denominator by dividing x^5 by x^3 - 125.

When you perform long division, you get a quotient and a remainder. The quotient becomes part of the oblique asymptote.

7. The remainder is usually a polynomial of a lower degree than the denominator. In this case, the remainder would be of degree 2 or less.

8. The equation of the oblique asymptote is the quotient obtained from long division. It represents the function's behavior as it approaches infinity or negative infinity.

In summary, to find the oblique asymptote for the given equation q(x) = x^5 / (x^3 - 125), you would divide x^5 by x^3 - 125 using long division and take the quotient as the equation of the oblique asymptote.