1-28 - and nishes draining just as the bucket reaches the...

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January 28, 2005 Announcements Exams will be returned in Section on Tuesday Detailed solutions are posted on the web under highlights. I will report on the overall class performance (statis- tics) and how to interpret your grade in Lecture on Monday. Today § 6.4: Work Problems § 6.5: Average Value of a Function 1
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Example 1: A circular reservoir has diame- ter 24m, the sides are 5m high, and the depth of the water is 4m. How much work is re- quired to pump all the water out over the side? (Use the fact that the density of the water is 1000kg/m 3 .)
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Example 2: ( § 6.4 #17) A leaky 10kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope that weights 0.8kg/m. Initially the bucket contains 36kg of water, but the water leaks at a constant rate
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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 b-a 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 )( b-a ) . Example 1: ( 6.5 #18) If a coee cup has temperature 95 C in a room where the tem-perature is 20 C, then, according to Newtons Law of Cooling, the temperature of the coee after t minutes is T ( t ) = 20 + 75 e-t/ 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 .

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1-28 - and nishes draining just as the bucket reaches the...

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