# How do you evaluate the limit #(3x^4-x^2+5)/(10-2x^4)# as x approaches #oo#?

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To evaluate the limit as x approaches infinity, we can focus on the highest power terms in the numerator and denominator. In this case, the highest power terms are x^4 in both the numerator and denominator. By dividing each term by x^4, we can simplify the expression:

(3x^4 - x^2 + 5) / (10 - 2x^4) = (3 - 1/x^2 + 5/x^4) / (10/x^4 - 2)

As x approaches infinity, 1/x^2 and 5/x^4 both approach zero, and 10/x^4 approaches zero as well. Therefore, the expression simplifies to:

(3 - 0 + 0) / (0 - 2) = 3 / -2 = -3/2

Thus, the limit of (3x^4 - x^2 + 5) / (10 - 2x^4) as x approaches infinity is -3/2.

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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.

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