# How do you find the Vertical, Horizontal, and Oblique Asymptote given #(x^2+1)/ (3x-2x^2)#?

Vertical asymptote

Horizontal asymptote

No slant asymptote.

Horizontal asymptote:

Slant or oblique asymptote : Since numerator is not one degree above the denominator polynomial, there is slant or oblique asymptote.

graph{(x^2+1)/(3x-2x^2) [-10, 10, -5, 5]}

By signing up, you agree to our Terms of Service and Privacy Policy

To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for (x). In this case, set (3x - 2x^2 = 0) and solve for (x).

To find horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is (y = 0). If the degree of the numerator is equal to the degree of the denominator, divide the leading coefficients to find the horizontal asymptote. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

To find oblique asymptotes, perform polynomial long division or synthetic division to divide the numerator by the denominator. The quotient represents the oblique asymptote. If the degree of the numerator is less than the degree of the denominator, there is no oblique asymptote.

So, for the function ( \frac{x^2+1}{3x-2x^2} ):

- Vertical asymptote: Set (3x - 2x^2 = 0) and solve for (x).
- Horizontal asymptote: Compare the degrees of the numerator and denominator.
- Oblique asymptote: Perform polynomial long division or synthetic division.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the Vertical, Horizontal, and Oblique Asymptote given #g(x)= (x+2 )/( 2x^2)#?
- How do you find the asymptotes for #f(x) = (3x^2 + 15x +18) /( 4x^2-4)#?
- How do you find the vertical, horizontal or slant asymptotes for #f(x) = (x^2 - 2x + 1)/(x)#?
- How do you determine if #h(x)=e^(|x|)# is an even or odd function?
- How do you determine if #f(x)=1+3x^3-x^5# is an even or odd function?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7