What is the average value of a function #f(x)=3x^2  2# on the interval #[0,2]#?
The average value of
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To find the average value of the function (f(x) = 3x^2  2) on the interval ([0,2]), follow these steps:
 Compute the definite integral of the function (f(x)) over the interval ([0,2]).
 Divide the result obtained in step 1 by the length of the interval, which is (2  0 = 2).
Let's calculate it:
 Compute the definite integral:
[\int_{0}^{2} (3x^2  2) , dx]

Integrate (f(x) = 3x^2  2) with respect to (x) from 0 to 2.

Evaluate the integral.

Divide the result by the length of the interval, which is 2.
The resulting value is the average value of the function (f(x)) over the interval ([0,2]).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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