Student (Print) SectionLast, First MiddleStudent (Sign)Student IDInstructorMATH 152Exam 3Fall 2000Test Form BPart I is multiple choice. There is no partial credit.Part II is work out. Show allyour work. Partial credit will begiven.You maynot use a calculator.1-9 /4510 /1011 /1512 /1013 /1014 /10TOTAL1Part I: Multiple Choice (5 points each)There is no partial credit. You maynot use a calculator.1.The series!n1."1nnisa.absolutelyconvergentb.convergent but not absolutelyconvergentc.divergentd.none of the above2.Determine the interval of convergence of the power series!n0.x3nn1.a.2,4¢b.¡2,4c."4,"2¢d.¡"4,"2e.".,.3.Compute!n0.3n52"na.253b.1253c.1252d.752e..24.Find the3rddegree Taylor polynomial forfxe"2xabout x1.a.e"22e"2x"12e"2x"1243e"2x"13b.e"2"2e"2x"12e"2x"12"43e"2x"13c.e"22e"2x"14e"2x"128e"2x"13d.e"2"2e"2x"14e"2x"12"8e"2x"13e.e"2"2e"2x"1"4e"2x"12"8e"2x"135.Compute!n0.n12n"1. HINT: Differentiate!n0.xn.a."4b."2c.49d.2e.46.Find the Maclaurin series for fxsin2x.a.2x"23x33!25x55!"27x77!Cb.2x"2x33!2x55!"2x77!Cc.x"x33!x55!"x77!Cd.xx33!x55!x77!Ce.2x2x33!2x55!2x77!C37.Find the equation of the circle for which one diameter has endpointsP1,1andQ7,9.a.x32y4225b.x32y425c.x"42y"5225d.x"32y"425e.x42y52258.Consider the triangle with verticesA0,0,0,B1,1,0andC0,2,2. Find the angle atA.a.0°b.30°c.45°d.60°e.90°9.Find a unit vector which is orthogonal to the plane containing the pointsP1,0,0,Q0,2,0,andR0,0,3.a.611,"311,211b.6,"3,2c.6,3,2d.67,"37,27e.67,37,274Part II: Work OutShow allyour work. Partial credit will begiven.You maynot use a calculator.10.(10 points) Determine if each of the followingseries converges or diverges. Saywhy.Be sure to name or quote the test(s)you use and check out all requirements of the test.If it converges, find the sum.If it diverges, does it divergeto.,".or neither?a.!n1.n"1n"nn1Circle one: Converges DivergesExplain:b.!n1.113nCircle one: Converges DivergesExplain:511.(15 points) Determine if each of the following series converges or diverges. Say why.Be sure to name or quote the test(s) you use and check out all requirements of the test.a.!n0."3nn!Circle one: Converges DivergesExplain:b.!n1."1n15n"1n24nCircle one: Converges DivergesExplain:c.!n2."1nnlnn2Circle one: Converges DivergesExplain:612.(10 points)a.Find the power series representation forfx11x2centered atx0and its radius ofconvergence.b.Find the power series representation forfxxtan"1xcentered atx0and its radius ofconvergence. HINT:tan"1x;0x11t2dt713.(10 points) Determine the interval of convergence of the power series!n1.x"2nn1/33n. Be sure toshow how you checked the convergence at the endpoints.14.(10 points) Find the volume of the parallelepiped with adjacent edgesPQ,PRandPS,
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