# What is the average value of the function #f(x)=2/x # on the interval #[1,10]#?

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To find the average value of the function (f(x) = \frac{2}{x}) on the interval ([1, 10]), we first find the definite integral of (f(x)) over that interval and then divide it by the length of the interval.

[ \text{Average value} = \frac{1}{b-a} \int_{a}^{b} f(x) , dx ]

In this case, (a = 1) and (b = 10).

[ \text{Average value} = \frac{1}{10-1} \int_{1}^{10} \frac{2}{x} , dx ]

Now, integrate (f(x)) with respect to (x) over the interval ([1, 10]).

[ \int_{1}^{10} \frac{2}{x} , dx = 2 \ln|x| \bigg|_{1}^{10} = 2(\ln|10| - \ln|1|) = 2(\ln(10)) = 2\ln(10) ]

Therefore, the average value of the function (f(x) = \frac{2}{x}) on the interval ([1, 10]) is (2\ln(10)).

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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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