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

This is supported by the following graph:

graph{ [-3.25, 16.75, -4.48, 5.52]} / (2x+1)^4/(3x^2+1)^2

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To find the limit of (2u+1)^4/(3u^2+1)^2 as u approaches infinity, we can use the concept of limits.

First, we divide both the numerator and denominator by u^4, which allows us to focus on the highest power terms.

This simplifies the expression to (2/u + 1/u^4)^4 / (3 + 1/u^2)^2.

As u approaches infinity, the terms with 1/u and 1/u^4 become negligible compared to the other terms.

Thus, the limit of the expression is (2/u)^4 / 3^2, which simplifies to 16/9.

Therefore, the limit of (2u+1)^4/(3u^2+1)^2 as u approaches infinity is 16/9.

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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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