CALC
1-28

# 1-28 - Announcements Exams will be returned in Section on...

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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 1000 kg/m 3 .)
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 0.8 kg/m. Initially the bucket contains 36kg of water, but the water leaks at a constant rate

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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 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 coﬀee cup has temperature 95 ◦ C in a room where the tem-perature is 20 ◦ C, then, according to Newton’s Law of Cooling, the temperature of the coﬀee after t minutes is T ( t ) = 20 + 75 e-t/ 50 . What is the average temperature of the coﬀee during the ﬁrst half an hour?...
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