quiz6-key - MATH 101\/210 Quiz#6 March 6 2014 Name Student Number Simplify your answers as much as possible Show your work This quiz is worth 6 marks 1[3

quiz6-key - MATH 101/210 Quiz#6 March 6 2014 Name Student...

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MATH 101/210: Quiz #6 March 6, 2014 Name: Student Number: Simplify your answers as much as possible. Show your work. This quiz is worth 6 marks. 1. [3 marks] Use the Comparision Theorem for Improper Integrals to determine whether the following integral isconvergent or divergent:I=Z1x3+ 2x4+x+ 1dx.We find a function to compare the integrand to as follows. For allx1,x3+ 2x4+x+ 1x3x4+x+ 1x3x4+x4+x4=13x0.Therefore by the Comparison Theorem, the improper integralIdiverges, since13Z1dxxis a divergentp-integral, withp= 1.2. Suppose thatf(0) = 1,f(1) = 3,f(2) = 0,f(3) =-1,f(4) = 0, and-4f(4)(x)3 for all 0x4.(a) [2 marks] CalculateS4(i.e., Simpson’s approximation toR40f(x)dxwithn= 4 intervals).

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