# Lim x->oo {x-(x^2)*ln((1+x)/x)} please explain all of phase...? thanks.

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This is still in an indeterminate form. Let's rewrite it:

Now, we can apply L'Hopital's rule and take the limit of the derivatives of the top and the bottom:

Now, we apply L'Hopital's rule again and take the derivatives of the top and the bottom:

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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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