# How do you evaluate # (t^3-2t+3)/ ( 5-2t^2 )# as t approaches infinity?

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To evaluate (t^3-2t+3)/(5-2t^2) as t approaches infinity, we need to consider the highest power of t in the numerator and denominator. In this case, the highest power of t is t^3 in the numerator and t^2 in the denominator.

As t approaches infinity, the term with the highest power of t will dominate the expression. Therefore, we can ignore the lower order terms.

Since t^3 grows faster than t^2 as t approaches infinity, we can simplify the expression by dividing both the numerator and denominator by t^3.

This simplification results in (t^3/t^3 - 2t/t^3 + 3/t^3) / (5/t^3 - 2t^2/t^3).

Simplifying further, we get (1 - 2/t^2 + 3/t^3) / (5/t^3 - 2/t).

As t approaches infinity, the terms with 2/t^2 and 5/t^3 become negligible compared to the other terms.

Therefore, the expression simplifies to 1 / (-2/t) = -t/2.

Thus, as t approaches infinity, the value of (t^3-2t+3)/(5-2t^2) approaches -t/2.

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As ( t ) approaches infinity, the expression ( \frac{t^3 - 2t + 3}{5 - 2t^2} ) can be evaluated by considering the dominant terms in the numerator and denominator. Since ( t ) is approaching infinity, the highest power terms in the expression become dominant. In this case, the highest power terms are ( t^3 ) in the numerator and ( -2t^2 ) in the denominator.

Therefore, as ( t ) approaches infinity, the expression simplifies to ( \frac{t^3}{-2t^2} ), which further simplifies to ( \frac{-1}{2t} ).

So, as ( t ) approaches infinity, ( \frac{t^3 - 2t + 3}{5 - 2t^2} ) approaches ( \frac{-1}{2t} ).

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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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