# How do you find the limit of #ln(t)^2/ (t)# as t approaches infinity?

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To find the limit of ln(t)^2 / t as t approaches infinity, we can use the limit properties and L'Hôpital's rule.

First, we rewrite the expression as (ln(t) / t) * ln(t).

Next, we apply L'Hôpital's rule by taking the derivative of the numerator and denominator separately.

The derivative of ln(t) is 1/t, and the derivative of t is 1.

So, the limit becomes (1/t) * ln(t) as t approaches infinity.

Now, we can apply the limit properties.

As t approaches infinity, 1/t approaches 0, and ln(t) approaches infinity.

Therefore, the limit of (1/t) * ln(t) 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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