# How do you find the vertical, horizontal or slant asymptotes for #C(t) = t /(9t^2 +8)#?

The denominator of C(t) cannot be zero as this would make C(t) undefined. Equating the denominator to zero and solving gives the value that t cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

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

To find the vertical asymptotes of the function ( C(t) = \frac{t}{9t^2 + 8} ), determine where the denominator equals zero. Set ( 9t^2 + 8 = 0 ) and solve for ( t ). In this case, the quadratic equation ( 9t^2 + 8 = 0 ) has no real solutions, so there are no vertical asymptotes.

To find horizontal asymptotes, compare the degrees of the numerator and the denominator. Since the degree of the denominator (2) is greater than the degree of the numerator (1), there is a horizontal asymptote at ( t = 0 ).

To determine if there are any slant asymptotes, divide the numerator by the denominator. Perform polynomial long division or use another method to divide ( t ) by ( 9t^2 + 8 ). If the quotient approaches a nonzero constant as ( t ) approaches positive or negative infinity, there is a slant asymptote. However, in this case, division results in a non-constant expression, so there is no slant 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 vertical, horizontal or slant asymptotes for #y= x / e^x#?
- What are some examples of unbounded functions?
- How do you determine if #f(x)= e^x# is an even or odd function?
- How do you determine if #g(x)=-3x^3+5# is an even or odd function?
- How do you determine if #f(x) = 1/x# 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