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Unformatted text preview: and nishes draining just as the bucket reaches the 12m level. How much work is done? Denition: 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 coee cup has temperature 95 C in a room where the temperature is 20 C, then, according to Newtons Law of Cooling, the temperature of the coee after t minutes is T ( t ) = 20 + 75 et/ 50 . What is the average temperature of the coee during the rst half an hour?...
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This note was uploaded on 03/09/2008 for the course CALC 1,2,3 taught by Professor Varies during the Spring '08 term at Lehigh University .
 Spring '08
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 Calculus

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