How do you identify all horizontal and slant asymptote for #f(x)=4/(x2)^3#?
The vertical asymptote is
The horizontal asymptote is
By signing up, you agree to our Terms of Service and Privacy Policy
To identify the horizontal and slant asymptotes for the function ( f(x) = \frac{4}{(x2)^3} ):

Horizontal asymptote:
 For rational functions, the horizontal asymptote can be determined by comparing 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, the horizontal asymptote is the ratio of the leading coefficients.
 In this case, the degree of the numerator is 0, and the degree of the denominator is 3, indicating that the denominator grows faster.
 Therefore, the horizontal asymptote is ( y = 0 ).

Slant asymptote (if applicable):
 Slant asymptotes occur when the degree of the numerator is exactly one more than the degree of the denominator.
 To find the slant asymptote, perform polynomial long division or synthetic division.
 Divide the numerator by the denominator, and the quotient obtained will be the equation of the slant asymptote.
 In this case, since the degree of the numerator is less than the degree of the denominator, there is no slant asymptote.
Therefore, for the function ( f(x) = \frac{4}{(x2)^3} ), the only asymptote is the horizontal asymptote ( y = 0 ).
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.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7