How do you find vertical, horizontal and oblique asymptotes for #f(x) =(x1)/(xx^3)#?
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is nonzero for these values then they are vertical asymptotes.
Oblique asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here hence there are no oblique asymptotes. graph{(1)/(x(x+1) [10, 10, 5, 5]}
By signing up, you agree to our Terms of Service and Privacy Policy
The line
The line
So the line
The oblique and horizontal ones are next:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the vertical asymptotes of the function f(x) = (x  1) / (x  x^3), we need to identify the values of x for which the denominator becomes zero, but the numerator does not. Setting the denominator equal to zero and solving for x gives us the potential vertical asymptotes.
To find horizontal asymptotes, we analyze the behavior of the function as x approaches positive and negative infinity. If the degrees of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the denominator is greater than the degree of the numerator, there is a horizontal asymptote at y = 0. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
To find oblique asymptotes, we perform polynomial long division or use other methods to divide the numerator by the denominator. If the result is a polynomial plus a proper rational function, the polynomial part represents the oblique asymptote.
Let's analyze f(x) = (x  1) / (x  x^3):
 Vertical asymptotes: Set the denominator equal to zero: x  x^3 = 0 x(1  x^2) = 0 x = 0 or x = ±1
So, the vertical asymptotes are x = 0, x = 1, and x = 1.

Horizontal asymptotes: The degrees of the numerator and denominator are the same (both are 1), so we compare their leading coefficients: Leading coefficient of the numerator = 1 Leading coefficient of the denominator = 1 Thus, the horizontal asymptote is y = 1/1 = 1.

Oblique asymptotes: Perform polynomial long division or divide (x  1) by (x  x^3) to determine if there's an oblique asymptote.
These are the methods to find the different types of asymptotes for the given function f(x) = (x  1) / (x  x^3).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 Prove that #(cosxcotx)/(1  sinx)  1 = cscx#?
 How do you determine if #g(x) = (4+x^2)/(1+x^4)# is an even or odd function?
 How do you determine if #y=2x^5+x# is an even or odd function?
 How do you find the inverse function of #f(x)=x/(x+1)#?
 How do you identify all asymptotes or holes for #y=(4x^3+32)/(x+2)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7