# How do you find the limit of #x/(ln(1+2e^x))# as x approaches infinity?

1

This is an indeterminate type so use l'Hopital's Rule. That is, find the limit of the derivative of the top divided by the derivative of the bottom.

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To find the limit of x/(ln(1+2e^x)) as x approaches infinity, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get (1)/(1+2e^x). As x approaches infinity, e^x also approaches infinity, so the limit becomes 1/(1+2∞), which simplifies to 1/∞. Therefore, the limit 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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