# How do you determine the limit of #[(n+5)/(n-1)]^n# as n approaches #oo#?

Write the expression as:

Now take the logarithm:

so that :

As:

as well, we have then:

Now, using the continuity of the exponential function:

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To determine the limit of [(n+5)/(n-1)]^n as n approaches infinity, we can use the concept of limits. By simplifying the expression, we get [(1+5/n)/(1-1/n)]^n. As n approaches infinity, both 5/n and 1/n approach zero. Therefore, the expression simplifies to (1/1)^n, which is equal to 1. Hence, the limit of [(n+5)/(n-1)]^n as n approaches infinity is 1.

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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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