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# CALC ANYL GEOM III MATH 126

UW

GPA 3.76

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This 2 page Class Notes was uploaded by Addison Beer on Wednesday September 9, 2015. The Class Notes belongs to MATH 126 at University of Washington taught by Matthew Conroy in Fall. Since its upload, it has received 18 views. For similar materials see /class/192069/math-126-university-of-washington in Mathematics (M) at University of Washington.

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Date Created: 09/09/15

Review Problems for Exam I MATH 126 7 Spring 2008 Here are some problems from old exams that will help you prepare for the midterml This is not intended to be an exhaustive review of the material You will be expected to understand how to do all the assigned homework I suggest you work these problems only after reworking most or all of the homework 1 9 F 5 0051533 50 Give the rst four nonzero terms of the Taylor Series expansion for f sin I based at El 4 The Taylor series for 91 based at b 0 is 17 91 1612 7 2513 What is gg0 Let e sinzl a Find the secondorder Taylor polynomial T2 for based at b 0 b Give a bound on the error 7 T2zl for z in the interval 701 S I S Olll Find the rst four nonzero terms of the Taylor series for 2 m 7 based at b 0 Let 3 7 7x 7 4x2 613 a Find the 2nd degree Taylor polynomial T2 for based at b 1 b Use the Quadratic Approximation Error Estimate to give an upper bound on the error 7 T2zl on the interval 075125 Give the coefficient on In in the Taylor series for ISEEZ based at b 0 Find the 2nd degree Taylor polynomial7 T2 for the function lnln I based at z el 2 sin 12 dz 0 by using the rst four nonzero terms of a Taylor series Give a decimal approximation of your result l Approximate the integral Write out the rst four terms of the Taylor series for the function 1 l fltxgt71513z Find the length of the curve 74 7 i1lttlt4 I7 y g 2t l Does the curve de ned by the polar equation Tsect9tant9 intersect the vertical line I 2 Explain HH 539 H 0 HH 90W H to N O to H Find the slope of the tangent line to the polar curve 1 76 0 r 6 gt at the point where it intersects the cartesian curve Find all points of intersection between the curve de ned by the polar equation 7 4 csc t9 and the line y I Find all values of I such that lt4 5 zgt and lt31 7 zgt are orthogonal Find a vector that is orthogonal to the vector 113 75gt and has length 7 Find the angle between the vectors 6 lt 7341 gt and I lt 311 gti Give a decimal value for the angler Suppose the vector lt z 3 2 gt is orthogonal to the vector lt 231 gti Find 1 The set of points that are twice as far from the origin as they are from the point 5 5 5 is a sphere Find its center and radiusi At what points is the tangent line to the curve I ttgtyt22t parallel to the line with parametric equations z3t5yt76 Eliminate the parameter in the following parametric equation pair to get a Cartesian equation for the curve that involves no trigonometric functions I costy sint icost Consider the curve de ned parametrically by the parametric equations 1 lnlnty lnti lnt Find the equation of the tangent line to the curve at the point t er

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