# How do you find the average rate of change of #s(t) = t^3 + t# over the interval [2,4]?

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To find the average rate of change of ( s(t) = t^3 + t ) over the interval ([2,4]), we use the formula:

[ \text{Average Rate of Change} = \frac{s(b) - s(a)}{b - a} ]

where ( a ) and ( b ) are the endpoints of the interval. Plugging in the values:

[ a = 2, \quad b = 4 ]

[ s(a) = (2)^3 + 2 = 10 ] [ s(b) = (4)^3 + 4 = 68 ]

[ \text{Average Rate of Change} = \frac{68 - 10}{4 - 2} = \frac{58}{2} = 29 ]

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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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