7thsol - Calculus 119 7th Week1 1. LowerEslimate = L5 = 5...

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7th Week 1 1. LowerEslimate = L 5 = 5 i =1 Δ xf ( x i - 1 ) = Δ x ( f ( x 0 ) + f ( x 1 ) + f ( x 2 ) + f ( x 3 ) + f ( x 4 )) = 5( f (0) + f (5) + f (10) + f (15) + f (20)) = 5( - 42 - 37 - 25 - 6 + 15) = - 475 UpperEstimate = R 5 = 5 i =1 Δ xf ( x i ) = Δ x ( f ( x 1 ) + f ( x 2 ) + f ( x 3 ) + f ( x 4 ) + f ( x 5 )) = 5( f (5) + f (10) + f (15) + f (20) f (25)) = 5( - 37 - 25 - 6 + 15 + 36) = - 85 2. g ( x ) = R x 2 tan x 1 2+ t 4 dt = R 0 tan x 1 2+ t 4 dt + R x 2 0 1 2+ t 4 dt = - R tan x 0 1 2+ t 4 dt + R x 2 0 1 2+ t 4 Let u = u ( x ) = tan x and v = v ( x ) = x 2 g ( x ) = - R u 0 1 2+ t 4 dt + R v 0 1 2+ t 4 g 0 ( x ) = - 1 2+ u 4 u 0 ( x ) + 1 2+ v 4 v 0 ( x ) = - 1 2+(tan x ) 4 sec 2 x + 1 2+( x 2 ) 4 2 x = - sec 2 x 2+tan 4 x + 2 x 2+( x ) 8 3. I = lim n →∞ 1 n ( s 1 n + s 2 n + ... + r n n ) =? 1 Please email all corrections and suggestions to these solutions to htor@metu.edu.tr. All solutions are available on the web at the url http://www.metu.edu.tr/
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7thsol - Calculus 119 7th Week1 1. LowerEslimate = L5 = 5...

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