Student (Print) SectionLast, First MiddleStudent (Sign)Student IDInstructorMATH 152Exam 3Spring2000Test Form APart 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.1-10 /5011 /1012 /1513 /1514 /10TOTAL1Part I: Multiple Choice (5 points each)There is no partial credit. You maynot use a calculator.1.Find the values of x such that the vectorsx,"1,3and2,"5,xare orthogonal.a."1 onlyb.0 onlyc.1 onlyd.0 and 1 onlye.1 and"1 only2.Compute limxv0ex3"1"x3x6HINT: The series for exmaybe helpful.a.0b.13!c."13!d.12e..3.Consider the parametric curvertt,sint,t3. Find parametric equations for the line tangentto the curve at t=.a.x1=t, y"t, z3=2=3tb.x1=t, y"1, z3=2=3tc.x=t, y"1tcost, z=33t3d.x=t, ytcost, z=33t3e.x=t, y"t, z=33=2t4.Find the Taylor series forfxx23aboutx2.a.74x"2x"22b.74x"22x"224x"23c.74x"2x"2223x"24Cd.74x"22x"224x"232x"24Ce.74x"22x"2223x"2343x"2425.The vectorsa,bandcb"aall lie inthe same plane as shown in the diagram.Which of the following statements is TRUE?a.ab0.b.abpoints into the page.c.abc0.d.bacpoints in the direction of"a.e.None of These6.Find a power series centered at x0 for the function fxx1"8x3, and determine its radiusof convergence.a.!n0."1n8nx3n1R18b.!n0."1n8nx3n1R8c.!n0.8nn!x3n1R2d.!n0.8nx3n1R18e.!n0.8nx3n1R127.Find the distance from the point3,"2,4to the center of the spherex"12y12z"224a.2b.3c.9d.61e.6138.Letfxsinx2. Computef140, the 14thderivative of fxevaluated at 0.HINT: Use a series for sinx2.a."114!7!b.7!14!c.14!7!d."14!7!e."14!7!9.Find the angle between the vectors u1,1,0and v1,2,1.a.0°b.30°c.45°d.60°e.90°10.Evaluate the integral;01/211x3dx as an infinite series.a.!n0."1n123n1"123126"129Cb.!n0.13n1123n11214241727110210Cc.!n0."1n3n1123n112"14241727"110210Cd.!n0."1n3n"1123n"1"2"222525"828Ce.!n0."1n3n"1123n"1"2"12221525"1828C4Part II: Work Out (points indicated below)Show allyour work. Partial credit will begiven.You maynot use a calculator.11.(10 points) Consider the planesP1:2x"yz1P2:xy"3z2a.(2 pts) Fill in the blanks:A normal to the plane P1isN1A normal to the plane P2isN2b.(3 pts) Find a vector parallel to the line of intersection of the two planes.c.(3 pts) Find a point on the line of intersection of the two planes.d.(2 pts) Find parametric equations for the line of intersection of the two planes.512.(15 points) Letfxlnx.a.(10 pts) Find the3rddegree Taylor polynomialT3forfxaboutx2.b.(5 pts) If this polynomialT3is used to approximatefxon the interval1txt3, estimatethe maximum error|R3|in this approximation usingTaylor’s Inequality.|Rnx|Mn1!|x"2|n1where Mufn1xfor1txt3.613.(15 points) Consider the pointsP1,0,"1, Q2,3,1andR0,4,1a.(5 pts) Find a vector orthogonal to the plane determined byP,QandR.b.(5 pts) Find the area of the triangle with verticesP,QandR.c.(5 pts) Find the equation of the plane determined byP,QandR.714.(10 points) Find the radius of convergence and the interval of convergence of the
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