Average value 233333333 233333 decimal average value

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Average Value 2.33333333 2.33333(decimal) , Average Value = (exact) Average Value 3.75 3.75000(decimal) , Average Value = (exact) Average Value 6.2 6.20000(decimal)(b) Determine the average value of the following functions on the interval [0,π/2]. Give your answers first in exact form, and then indecimal form with at least three decimal digits., Average Value = (exact) Average Value 0.63661977 0.63662(decimal) , Average Value = (exact) Average Value 0.5 0.50000(decimal) , Average Value = (exact) Average Value 0.42441318 0.42441(decimal) y= xy= x2y= x3y= x4y= cos xy= cos2xy= cos3x
11/17/14, 2:17 PMMath 125 HW_5CPage 8 of 8, Average Value = (exact) Average Value 0.375 0.375(decimal)(c) The average values in part (a) increased, while the average values in part (b) decreased. The reason for this is thaty= cos4xthe interval [1,2] is shorter than the interval [0,π/2].each function in part (a) is an increasing function of xin [1,2], while each function in part (b) is a decreasing function of xin[0,π/2]. when y> 1, we have y< y2< y3< y4, while when 0 < y< 1, we have y> y2> y3> y4.
11/17/14, 2:17 PMMath 125 HW_6APage 1 of 7Current Score :55 / 55Due : Thursday, May 15 2014 11:00 PM PDT1.10/10 points | Previous Answersscalcet7 7.4.003.nvaWrite out the form of the partial fraction decomposition of the function (See Example). Do not determinethe numerical values of the coefficients.(a) (b) Solution or ExplanationClick to View SolutionMath 125 HW_6A (Homework)ZHENG ZHOUMath 125 Spring 2014, section D, Spring 2014Instructor: Ethan DevinatzWebAssignThe due date for this assignment is past.Your work can be viewed below, but no changes can be made.x4+ 4x5+ 4x34(x225)2
11/17/14, 2:17 PMMath 125 HW_6APage 2 of 72.5/5 points | Previous AnswersSCalcET7 7.4.012.Evaluate the integral.Solution or ExplanationMultiplying both sides by to get The coefficients of xmust be equal and the constant terms are also equal, so and Adding twice the first equation to the second gives us andhence, Thus,Another Method:Substituting 5 for xin the equation gives Substituting 2 for xgives 3.5/5 points | Previous AnswersSCalcET7 7.4.013.Evaluate the integral. (Remember to use ln |u| where appropriate. Use Cfor the constant ofintegration.)Solution or ExplanationClick to View Solutiondx1x8x27x+ 100= + .x8x27x+ 10Ax2Bx5(x2)(x5)x8 = A(x5) + B(x2) x8 = Ax5A+ Bx2Bx8 = (A+ B)x+ (5A2B).A+ B= 15A2B= 8.A= 2 A= 2,B= 1.= = 2ln|x2| ln|x5|= (0 ln 4) (2ln 2 ln 5)dx1x8x27x+ 100dx12x21x5010x8 = A(x5) + B(x2)1 = B.2 = AA= 2.dxaxx2bx
11/17/14, 2:17 PMMath 125 HW_6APage 3 of 74.5/5 points | Previous AnswersSCalcET7 7.4.017.Evaluate the integral.Solution or ExplanationSetting y= 0 gives Setting gives Setting y= 3gives Nowdy24y27y12y(y+ 2)(y3)1= + + 4y27y12y(y+ 2)(y3)AyBy+ 2Cy34y27y12 = A(y+ 2)(y3) + By(y3) + Cy(y+ 2).

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