# How do you find the Vertical, Horizontal, and Oblique Asymptote given #(x^3+4)/(2x^2+x-1)#?

The vertical asymptotes are

The oblique asymptote is

No horizontal asymptote

Let start by factorising the denominator

Let's do a long division

Therefore,

graph{(y-(x^3+4)/(2x^2+x-1))(y-x/2+1/4)=0 [-18.02, 18.03, -9, 9.02]}

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

To find the vertical asymptotes, factor the denominator and identify any values of ( x ) that make the denominator equal to zero. These values represent vertical asymptotes.

To find the horizontal asymptote, 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 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 than the degree of the denominator, there is no horizontal asymptote.

For oblique asymptotes, perform polynomial long division. If the division results in a non-zero remainder, there is an oblique asymptote given by the quotient. If the remainder is zero, there is no 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.

- How do you find the inverse of #h(x)= x^3 - 3x^2 + 3x - 1# and is it a function?
- How do you find the slant asymptote of # (2x^3+2x)/(x^2-1) #?
- How do you find the domain and range and is it a function given points #{(0,0), (2,2), (2,-2), (5,8), (5,-8)}#?
- How do you determine if #f(x) = x^3 - x^5# is an even or odd function?
- How do you find the vertical asymptotes and holes of #f(x)=1/(x^2+5x+6)#?

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