# How do you find the limit of #(3 x^4 + 4) / ((x^2 - 7)(4 x^2 - 1)) # as x approaches #oo#?

Expand the denominator:

As they are of the same degree, the limit is finite and equals the ratio of the leading coefficients:

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

To find the limit of the given expression as x approaches infinity, we need to analyze the highest power terms in the numerator and denominator. In this case, the highest power terms are x^4 in the numerator and x^2 in both denominators.

By dividing every term in the expression by x^4, we can simplify it to:

(3 + 4/x^4) / ((1 - 7/x^2)(4 - 1/x^2))

As x approaches infinity, the terms with 1/x^4 in the numerator become negligible. Similarly, the terms with 7/x^2 and 1/x^2 in the denominators also become negligible.

Thus, the simplified expression becomes:

(3 + 0) / (1 * 4)

Therefore, the limit of the given expression as x approaches infinity is 3/4.

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 determine the limit of #(2)/(x-3)# as x approaches #3^-#??
- How do you use the limit definition to prove a limit exists?
- How do you find the limit of #sec3xcos5x# as x approaches infinity?
- How do you find the limit of #(x^2 - 64) / ((x^(1/3)) -2)# as x approaches #8#?
- How do you find the limit of #x^3-x# as x approaches #0^+#?

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