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TAMU MATH 152 - 152e3a

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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 vectorsx,"1,3and2,"5,xare 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 curvertt,sint,t3. Find parametric equations for the line tangentto the curve at t=.a.x1=t, y"t, z3=2=3tb.x1=t, y"1, z3=2=3tc.x=t, y"1tcost, z=33t3d.x=t, ytcost, z=33t3e.x=t, y"t, z=33=2t4.Find the Taylor series forfxx23aboutx2.a.74x"2x"22b.74x"22x"224x"23c.74x"2x"2223x"24Cd.74x"22x"224x"232x"24Ce.74x"22x"2223x"2343x"2425.The vectorsa,bandcb"aall lie inthe same plane as shown in the diagram.Which of the following statements is TRUE?a.ab0.b.abpoints into the page.c.abc0.d.bacpoints in the direction of"a.e.None of These6.Find a power series centered at x0 for the function fxx1"8x3, and determine its radiusof convergence.a.!n0."1n8nx3n1R18b.!n0."1n8nx3n1R8c.!n0.8nn!x3n1R2d.!n0.8nx3n1R18e.!n0.8nx3n1R127.Find the distance from the point3,"2,4to the center of the spherex"12y12z"224a.2b.3c.9d.61e.6138.Letfxsinx2. Computef140, the 14thderivative of fxevaluated at 0.HINT: Use a series for sinx2.a."114!7!b.7!14!c.14!7!d."14!7!e."14!7!9.Find the angle between the vectors u1,1,0and v1,2,1.a.0°b.30°c.45°d.60°e.90°10.Evaluate the integral;01/211x3dx as an infinite series.a.!n0."1n123n1"123126"129Cb.!n0.13n1123n11214241727110210Cc.!n0."1n3n1123n112"14241727"110210Cd.!n0."1n3n"1123n"1"2"222525"828Ce.!n0."1n3n"1123n"1"2"12221525"1828C4Part 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"yz1P2:xy"3z2a.(2 pts) Fill in the blanks:A normal to the plane P1isN1A normal to the plane P2isN2b.(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) Letfxlnx.a.(10 pts) Find the3rddegree Taylor polynomialT3forfxaboutx2.b.(5 pts) If this polynomialT3is used to approximatefxon the interval1txt3, estimatethe maximum error|R3|in this approximation usingTaylor’s Inequality.|Rnx|Mn1!|x"2|n1where Mufn1xfor1txt3.613.(15 points) Consider the pointsP1,0,"1, Q2,3,1andR0,4,1a.(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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TAMU MATH 152 - 152e3a

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