# What is the limit of #(1+4/x)^x# as x approaches infinity?

This is an indeterminate type so we 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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The limit of (1+4/x)^x as x approaches infinity is e^4.

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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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