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Unformatted text preview: and ﬁnishes draining just as the bucket reaches the 12m level. How much work is done? Deﬁnition: Let f be a continuous function on [ a, b ]. The average value of f on [ a, b ] is 1 ba Z b a f ( x ) dx. Mean Value Theorem for Integrals: Let f be a continuous function on [ a, b ]. There exists c ∈ [ a, b ] such that Z b a f ( x ) dx = f ( c )( ba ) . Example 1: ( § 6.5 #18) If a coﬀee cup has temperature 95 ◦ C in a room where the temperature is 20 ◦ C, then, according to Newton’s Law of Cooling, the temperature of the coﬀee after t minutes is T ( t ) = 20 + 75 et/ 50 . What is the average temperature of the coﬀee during the ﬁrst half an hour?...
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 Spring '08
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 Calculus, Derivative, Mean

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