# How do you find the Limit of # (ln x)^2 / (3x )# as x approaches infinity?

0

on inspection you can see that the logarithmic numerator is going to grow more slowly than the denominator

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so

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To find the limit of (ln x)^2 / (3x) as x approaches infinity, we can use the limit properties and L'Hôpital's rule.

First, we rewrite the expression as (ln x / x) * (ln x / 3).

As x approaches infinity, ln x also approaches infinity.

Using L'Hôpital's rule, we differentiate the numerator and denominator separately.

The derivative of ln x is 1/x, and the derivative of x is 1.

Taking the limit as x approaches infinity, we get (1/x) / 1, which simplifies to 0.

Therefore, the limit of (ln x)^2 / (3x) as x approaches infinity is 0.

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