How do you find vertical, horizontal and oblique asymptotes for #R(x) = (6x^2 + x + 12)/(3x^2 - 5x - 2)#?
vertical asymptotes
horizontal asymptote y = 2
Since the denominator of R(x) is undefined, it cannot be zero. By solving for the denominator, one can determine the values that x cannot be. If the numerator of these values is non-zero, the values are vertical asymptotes.
As horizontal asymptotes arise,
There are no oblique asymptotes in this case (both of degree 2), as oblique asymptotes arise when the degree of the numerator > degree of the denominator. graph{(6x^2+x+12)/(3x^2-5x-2) [-10, 10, -5, 5]}
By signing up, you agree to our Terms of Service and Privacy Policy
Vertical asymptotes: Set the denominator equal to zero and solve for x. The values of x obtained are the vertical asymptotes.
Horizontal asymptote: Compare the degrees of the numerator and the denominator. If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is y = 0. If the degrees are equal, divide the leading coefficients of the numerator and denominator to find the horizontal asymptote. If the degree of the numerator is greater, there is no horizontal asymptote.
Oblique asymptote: Perform polynomial long division to divide the numerator by the denominator. The quotient obtained represents the oblique asymptote.
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.
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 determine whether the graph of #y^2=x^2# is symmetric with respect to the x axis, y axis or neither?
- How do you find vertical, horizontal and oblique asymptotes for #(x+4)/(3x^2+5x-2)#?
- How do you find the vertical, horizontal or slant asymptotes for #f(x)=(5x-15)/(2x+4) #?
- How do you describe the transformation of #f(x)=x^3+7# from a common function that occurs and sketch the graph?
- How do you find vertical, horizontal and oblique asymptotes for #(3x^2+2x-5)/(x-4)#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7