# How do you find the limit of #(1+7/x)^(x/10)# as x approaches infinity?

There are other method available, but I use

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To find the limit of (1+7/x)^(x/10) as x approaches infinity, we can use the property of exponential limits.

First, we rewrite the expression as e^(ln((1+7/x)^(x/10))).

Next, we take the natural logarithm of both sides to simplify the expression further.

Using the properties of logarithms, we can rewrite the expression as (x/10) * ln(1+7/x).

Now, we can evaluate the limit as x approaches infinity.

As x approaches infinity, 7/x approaches 0, and ln(1+7/x) approaches ln(1) which is 0.

Therefore, the limit becomes (x/10) * 0, which is equal to 0.

Hence, the limit of (1+7/x)^(x/10) as x approaches infinity 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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