# How do you find #lim (t^3-6t^2+4)/(2t^4+t^3-5)# as #t->oo#?

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Finding the limit of a function is basically just a way to find out what value we get closer and closer to as we approach a certain number.

Finding the limit at infinity is no different. We should establish a couple of rules before we start.

Knowing this, we can go ahead and approach the problem as follows:

So, in our final step, we look at our rules that we noted above and simplify. Applying our rules, we get the following answer:

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To find the limit as t approaches infinity of the expression (t^3-6t^2+4)/(2t^4+t^3-5), we need to determine the behavior of the expression as t becomes very large.

First, we observe that the highest power of t in the numerator and denominator is t^4. Dividing both the numerator and denominator by t^4, we get (1/t + -6/t^2 + 4/t^4)/(2 + 1/t - 5/t^4).

As t approaches infinity, the terms with 1/t and 1/t^2 in the numerator become negligible compared to the higher powers of t. Similarly, the terms with 1/t and 1/t^4 in the denominator also become negligible compared to the constant term 2.

Therefore, the expression simplifies to (0 + 0 + 4/t^4)/(2 + 0 - 0), which further simplifies to 4/t^4 divided by 2.

As t approaches infinity, 4/t^4 approaches 0, and dividing 0 by 2 gives us the final result of 0.

Hence, the limit of (t^3-6t^2+4)/(2t^4+t^3-5) as t approaches infinity is 0.

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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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