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**8.2 Volume and Average Value**

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**DEFINITION: Let f be a continuous function over a closed interval**

[a, b]. Its average value, yav, over [a, b] is given by

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**Example: Find the average value**

Of f(x) = x2 over the interval [0, 2].

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**Example: Find the average value of f(x) = x2 over**

the interval [0, 2].

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**Find the average value of the function over the given interval:**

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A group of marine biologists estimates that if certain conservation measures are implemented, the population of an endangered species of whale will be where N(t) denotes the pop at the end of year t. Find the average pop of the whales over the next 10 years.

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The sales of the USI company in the first t years of its operation are approximated by where S(t) is measured in millions of dollars. What were the average sales over the first 5 years?

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**(c) Explain the difference in (a) & (b).**

The cost function for a certain product is (a) Find the average cost per unit for 500 units. (b) Find the average value of the cost function over the interval [0, 500 ]. (c) Explain the difference in (a) & (b).

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3.9 Differentials Let y = f(x) represent a function that is differentiable in an open interval containing x. The differential of x (denoted by dx) is any.

3.9 Differentials Let y = f(x) represent a function that is differentiable in an open interval containing x. The differential of x (denoted by dx) is any.

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