# How do you find any asymptotes of #h(x)=(x-5)/(x^2+2x-4)#?

By (a) seeing if the denominator is zero for any value(s) of

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

To find the asymptotes of the function h(x) = (x-5)/(x^2+2x-4), we need to consider the behavior of the function as x approaches positive or negative infinity.

First, we check for vertical asymptotes by finding the values of x that make the denominator equal to zero. Solving x^2+2x-4 = 0, we find that x = -1 ± √5. Therefore, there are two vertical asymptotes at x = -1 + √5 and x = -1 - √5.

Next, we check for horizontal asymptotes by examining the degrees of the numerator and denominator. Since the degree of the numerator is 1 and the degree of the denominator is 2, we have a slant asymptote instead of a horizontal asymptote. To find the slant asymptote, we perform long division or synthetic division to divide the numerator by the denominator.

Performing the division, we get h(x) = 1 - (3x + 11)/(x^2 + 2x - 4). The quotient is 1 and the remainder is -(3x + 11)/(x^2 + 2x - 4). As x approaches positive or negative infinity, the remainder approaches zero. Therefore, the slant asymptote is y = 1.

In summary, the function h(x) = (x-5)/(x^2+2x-4) has two vertical asymptotes at x = -1 + √5 and x = -1 - √5, and a slant asymptote at y = 1.

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 Limit of #x+3# as #x->2# and then use the epsilon delta definition to prove that the limit is L?
- How do you find the limit of # (1)/(x-2)# as x approaches #2^+#?
- What are the asymptotes of #f(x)=(x^2+1)/(x^2-9)#?
- How do you evaluate the limit #cos((x^5+1)/(x^6+x^5+100))# as x approaches #-oo#?
- How do you find the limit of #(sin2x)/x# as x approaches infinity?

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