# How do you find the limit #lnx/sqrtx# as #x->oo#?

As we have:

The limit:

so:

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To find the limit of ln(x)/sqrt(x) as x approaches infinity, we can use L'Hôpital's rule. Taking the derivative of the numerator and denominator separately, we get (1/x)/(1/2sqrt(x)). Simplifying this expression, we have 2sqrt(x)/x. As x approaches infinity, the term 2sqrt(x) grows faster than x, so the limit of ln(x)/sqrt(x) as x 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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