# How do you find the limit of #(lnx)^2/sqrtx# as #x->oo#?

The limit:

and again:

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To find the limit of (lnx)^2/sqrtx as x approaches infinity, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get:

d/dx (lnx)^2 = 2lnx/x d/dx sqrtx = 1/(2sqrtx)

Now, we can rewrite the expression as:

lim(x->oo) (2lnx/x) / (1/(2sqrtx))

Simplifying further:

lim(x->oo) (4lnx) / x^(3/2)

As x approaches infinity, the numerator (4lnx) grows without bound, while the denominator (x^(3/2)) also grows without bound. Therefore, the limit of (lnx)^2/sqrtx as x approaches infinity is infinity.

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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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