65 - a. estimate the average velocity of the car during the...

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MTH 173 section 6.5 notes page 1 Average value of a function Defn: The average value of a function on the interval is 0 0 +ß , ave c d 0 o 0 B .B " ,  + ave ( a b + , 2. Determine the average value of in 0 B o "ß % " B a b c d 0 o .B o B o %  " o " " " " % %  " B $ $ $ ave ( º a b " % " % ln ln ln ln The Mean Value Theorem for Integrals: If is continuous on then there is a 0 +ß , ß c d number in such that - +ß , c d 0 - ,  + o 0 B .B a ba b a b ( + , 10. Given in the interval 0 B o B !ß % a b c d È a. Determine the average value of on the interval 0 0 o B.B o o % o o " " #B " ) % %  ! % $ ' ' $ ave ( È » ˆ ! % $Î# ! % $Î# b. Determine such that - 0 o 0 - ave a b % % "' $ $ * o 0 o 0 - o - Ê - o o ave a b È O  # c. Sketch the graph of and a rectangle whose area is the same as the area under the 0 graph of . 0
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MTH 173 section 6.5 notes page 2 ( 16 9 , 4 3 ) this line is x= 16 9 16. The velocity graph of an accelerating car is shown.
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Unformatted text preview: a. estimate the average velocity of the car during the first 12 seconds. We can estimate the distance traveled by estimating the area under the curve. We can estimate the area with trapezoids, as shown MTH 173 section 6.5 notes page 3 The trapezoids are rectangles with triangles on top, so we estimate: ft/s > ! # % ' ) "! "# @ ! ") $' %) &) '' (! @ ! #' &# (! )& *& *( areas: region average height area total area distance " "$ #' # $* () $ '" "$# % (( "&% & *! ")! ' *' "*# o ('# @ o o '$ o %% ('# "# ave = ft/s mph distance traveled time change b. At what time was the instantaneous velocity equal to the average velocity? at about 5 seconds...
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This note was uploaded on 09/17/2009 for the course MTH Calc taught by Professor Bush during the Spring '09 term at Northern Virginia.

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65 - a. estimate the average velocity of the car during the...

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