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# 538 Study Guide for MA 22200 at Purdue

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Date Created: 02/06/15

Purdue University Study Guide for MA 222 For students who plan to obtain credit in MA 221 by examination Textbook Technical Calculus 4th edition by Peter Kuh ttig3 BrooksCole When you are ready for the examination obtain the proper form from your academic advisor Follow the instructions on the form To prepare for the exam you should obtain from the MA 222 course web page or the Undergraduate Services Of ce MATH 242 1 The assignment sheet 2 The nal exam practice problems 3 The nal exam formula page The address of the course web page is httpwww mothpurdoe edccourscsma222 The assignment sheet lists the sections of the text that are covered in the course The homework problems from the assignment sheet and the nal exam practice problems pro vide good preparation for the examination The nal exam formula page will be attached to the exam A calculator with exponential logarithmic and trigonometric functions will be needed for the exam Any brand of oneline calculator may be used However no multiline calculators are allowed Cell phones and PDA S may not be used as a calculator MA 222 Assignment Sheet Fall 2006 Text Technical Calculus with Analvtic Geometerv by Peter Kuh ttig Fourth Edition BrooksCole 2005 A calculator with trigonometric and logarithmic functions and their inverses is required Calculators may be used when appropriate on the assignments below Graphing calculators or programmable calculators may not be used on quizzes or exams Lessons Sections Assignment 1 61 3 Review p218 717213538 p222 9213358 p251 910 2 66 p232 147 11 14 1520 22 232528 30 33 38 434647 3 67 p237 28131516222832 4 68 p240 167 17 18 2021 2530 45 5 610 p247 13710131617 6 71 p254 145 67 9 12 132532 7 72 p257 347 10 15 19 20 29 3848 50 8 73 p260 23 9 10 17 22 28 31 33 3442 9 78 p287 125 9 10 12 10 78 p288 18 19 20 21 22 Just give the partial fraction expansion Do not integrate 11 REVIEW FOR EXAM 1 12 EXAM 1 IN CLASS 13 79 p290 123 4 7 8 11 12 14 79 p290 13 14 17 19 22 2427 28 15 p291 Review Exercises 1 2 57 10 11 13 22 26 41 16 101 p365 124 57 10 12 1520 17 103 p376 1258 12 18 104 p380 14 5 7 9 12 13 14 18 19 105 p386 145 9 12 13 14 20 105 p386 15 17 1921 25 27 21 106 p397 1234 22 106 p397 5678 p398 26 23 111 p402 245 9 13 15 18 20 24 77CATCH UP77 ANDOR STRUCTURED REVIEW FOR EXAM 2 25 OPTIONAL REVIEW FOR EXAM 2 EVENING EXAM 26 112 p407 158 9 11 13 15 2133 3536 27 113 p412 2591215252936 28 114 p419 367 8 12 13 29 114 p419 14 16 1522 24 26 30 121 p431 247 9 11 12 14 2930 31 122 p434 1451011151721454647 32 123 p440 15781014 15 1620 33 123 p441 21 242527 2930353740 34 124 p449 1 23 4 5 9 10 11 14 15 16 35 p450 Review Exercises 48 12 15 1721 22 25 36 REVIEW FOR EXAM 3 37 EXAM 3 IN CLASS 38 1317 3 p459 23 5 7 10 12 39 1317 3 p459 14 16 1920 21 24 40 1317 3 p459 37 38 3942 45 48 41 134 p464 157 8 11 12 14 42 134 p464 16 17 18 19 21 2428 43 REVIEW FOR FINAL EXAM q 4 REVIEW FOR FINAL EXAM MA 222 Final Exam Practice Problems The Table of Integrals pages 481 484 of the text and the Formula Page may be used They will be attached to the nal exam 1 10 11 12 13 If y lnsecz The velocity of an object falling through a resisting medium is given by v 1001 7 sin2z 39 Find f IrQ iffz a A 727139 B 747139 C 27r D 7139 E 7r8 then 27y 13 A cosz B lnsecztanz C sinz D tanm E secz Express as a single logarithm ln 3 7 ln A lnx37E B1ngz G 1mm Dln3m7 E lnz If y ea 2 calculate y 2 2 2 A 2m B 52 C 25 1 D 2me2 E e If y ln x 1 calculate 3 2m m 1 A B D E None of these xm21 xm21 m2l 2m21 Find an equation for the tangent line to the curve 5y 1 2 2 at the point 1 0 Aym71By2m72 Cy72z2 Dy7m1Ey72x72 Find the maximum value of the function x 2 ln2m A 1B 2 C2eD2E 25 Which of the following best describes the function y lnz 7 z A There is a relative minimum at z 1 and the curve is concave down for all z gt 0 B There is a relative maximum at z 1 and the curve is concave down for all z gt 0 C There is a relative maximum at z 1 the curve is concave down for 0 lt z lt 1 and concave up for z gt 1 D There is a relative minimum at z 1 the curve is concave down for 0 lt z lt 1 and concave up for z gt 1 E None of these 57000115 Find the acceleration when t 100 Give your answer correct to two decimal places A 009 B 952 C 9048 D 038 E 114 Find 3 if y z cos 2x A 7m sin 2x cos 2x B 72msin 2x cos 2x C x sin 2x cos 2x D 2x sin 2x cos 2x E 72 sin 2x cos 2x E 1 t mdz vauae 7 xl7m2 Azlnl17z2l0 B217x2C C7lnll7m2l0 D717z2C ENoneof these Evaluate ya m 17 A6lnlz5llnlz1l0 B31nz2lnlzlC c31nlz2zl0 D1nz7lnlz1l0 Elnlx2llnlm1l0 Evaluate Give your answer correct to 3 decimal places 2 dz 1 935274 MA 222 14 15 16 17 18 19 20 21 22 23 Final Exam Practice Problems A 0800 B 0267 C 2401 D 0928 E 0743 3 Evaluate xEln zdm Give your answer correct to 2 decimal places 1 A 194 B 150 C 7021 D 101 E 127 Evaluate sin5 3x dz using a reduction formula A 7sin4 3mcos 3x 7 cos 3msin2 3x 2 C B 71178cos6 3x C C 7sin4 3zcosz z 7 i sin 6x 1 sin12z C D 7171Esin4 3zcos 3x 7 cos 3msin2 3x 2 C E None of these Find the area of the region bounded by the graph of y sin 2m the z axis7 and the lines z 0 and z A 2 B 1 C 0 D l E E 2 4 Find the rst three non zero terms of the Maclaurin series of fz x1 1 3m A 1 3x7gm2 B 1x13x7 13z C 1 ix7 m2 D fm1gx1 37 glt1 3x E m 17 m2 Using the Maclaurin series ln1 z z 7 z2 z3 7 ix zg 7 nd the minimum number of terms required to calculate ln13 so that the error is g 0001 A2 B3 04 D5 E6 Find the rst three non zero terms in the Taylor series for fz sin A 1 00 l 95 3 95732 B 1 205 3 C 1 00 m i e 33 06 35 D 1 WE he 3 105 2l E None of these owers of m 7 03 Approximate cos dz using three terms of the appropriate Maclaurin series Give your 0 answer correct to 4 decimal places A 08538 B 02779 G 09553 D7 02955 E 01863 If f is a periodic function of period 27139 and 0 for 77139 g z lt 0 1for0 z 0 forgltm 7r 1W calculate the rst three non zero terms of the Fourier series for That is7 the rst three non zero terms in the series 010 a1 cosz bl sinz a2 cos 2x 112 sin 2x 1 A gcosmsinz B icosz7 sinz C i 7 cosz cos2z D Z icosz isinm E None of these Find the general solution of the differential equation y2dz m 12dy 0 1 1 Am13y30 B CClnlx1llnlylC z1 1 D2m12yC Em7C y 1 Find the particular solution of the differential equation 3 7y z2 where y 2 when x 1 1 2 MA 222 24 25 26 27 28 29 30 31 32 33 34 35 Final Exam Practice Problems m4 7 m3 5 m3 7 m3 7 Ayj1 By CyIE Dyj1 ENoneofthese Find the particular solution of the differential equation y y 7 6y 0 where y 0 and y71whenm0 A y 752573 352 B y 72530 3572 C y 7e 3 52 D y 753E 1 5 2 E None of these Find the general solution of the differential equation D2y 7 Dy 1 y O A y 0151 2 0251 2 B y e 01 sin3m2 02 cos3z2 C y e cl sin3m 02 cos3z D y sac2 01 sin3z2 02 cos3z2 E None of these Find the equation of the orthogonal trajectories of the curves y czf A 15cz3y1 Bz25y2c Cy 6 Dlnlyllnlmlc E50yx471 15m3 Find the equation of the curve for which the slope at any point z y is z y and which passes through the point 07 1 Ay2e 7x71Bye z2 Cy7x1Dy2e 7x71Eye z An object moves with simple harmonic motion according to the equation 2172 64x 0 Find the displacement x as a function oft if z 4 and Z7 3 when t O A z 4sin8t cos8t B x 3sin8t 4cos8t C x 6731 sin64t 4cos64t D x gsin8t 4cos8t E z 8sin8t 4cos8t Find the general solution of the differential equation D2y 8Dy 16y O A y 6167462574w B y 61646264w C y clei4w02574w D y cl sin 4m62 cos 4m E y 0154 3267406 Calculate the Laplace transform of 25 5 sin 4t 8 8 8 2 A B C D E s73216 s32 16 s73216 s3s216 s32 16 i 23 Calculate the inverse Laplace transform of A 1710454 5 7 at B 4e 4t at C 615 e t D 45 e t E None of these Calculate the Laplace transform of the expression y 7 33 2y7 where y m f0 71 and f 0 2 A 8273s2Lf B 32Lfs72 C 3273s2Lfs71 D 3273s2Lfs1 E 3273s2Lf 375 Find the Laplace transform of the solution of the differential equation 3 1 2y 5 2 5 1 2 1 2 1 1 y02 A7 2 C D E 322 s2 s2s22 3721972 3722 Use Laplace transforms to solve the differential equation y 1 9y 3t y0 17 y 0 71 A y t7 gsin3t cos3t B y it 7 17sin3t cos3t C y 4cos3t 7 sin3t D y cos3t 7 g sin3t E None of these Use Laplace transforms to solve the differential equation D2y 7 2Dy y at 240 0720 0 A y 2t2et B y i295 C y 265 D y t2e t E y 2te t 3 MA 222 36 37 38 39 40 Final Exam Practice Problems 8 1f 8 8 71gt2lts 2 B and C are constants which of the following is the partial fraction expansion of f3 A7 A A B C A B C A3 B3 C3 3931 31 32 39312 32 3931 312 32 D A B C E A B 3931 312 32 3931 32 A body whose temperature is 30 C is placed in a room whose temperature is 5 C After two minutes the temperature of the object has dropped to 27 C How long will it take for the temperature to drop tp 15 C A 935 min B 125 min C 1434 min D 862 min E 1733 min If the current in an AC circuit is given by i cost sin 25 then the rst maximum of the current after t 0 is A2A n A C1A D2A EgA A certain radioactive substance decays according to the law N 65 2 57 where N in kilograms is the amount present and t is the time in years Find the time rate of change of N with respect to if when t 27 rounded to the nearest hundredth A 022 B 002 C 002 D 022 E 0012 Find the current7 i as a function of time7 t for a LC circuit with L 1 H and C 10 x 10 4 F7 if you know that 5t E 07 and i 10 and q 0 when t 0 A 100 cos 10t B 10 cos 100t C 01 sin 100t D 100 sin 10t E 10 sin 100t Answers 1 B 2 D 3 E 4 A 5 C 6 C 7 E 8 B 9 A 10 B 11 D 12 E 13 B 14 A 15 D 16 B 17 E 18 C 19 A 20 B 21 D 22 B 23 C 24 A 25 D 26 B 27 D 28 D 29 A 30 B 31 B 32 E 33 C 34 A 35 C 36 D 37 C 38 D 39 A 40 B MA 222 FORMULAS Table of Laplace Transforms f0 F8 f0 F8 1 n 1 1 9 t at 7 3 e 3 an1 1 02 2 t 8 2 10 1 7 cosat W n 03 3 t 11 t7 i t 8n1 1 sma 3232 12 1 2 3 4 eat 12 sin at 7 at cos at L s 7 a 32 a22 2 5 sin at L 13 tsin at i 32 02 82 022 6 s 4 2032 cos at 82 12 1 Sin 01 at cos at 82 012 b 32 7 02 t 7 6 Sin bt m 15 tcosat m t s 7 a 8 6 cos bt m Laplace Transforms of Derivatives Ly 3Ys 7 3107 Ly 3213 7 3110 7 yO Where Ys Linear differential equations y PIy has solution y Where yef 13mm fQIefPzdzdIO Taylor Series fc fcx 7 c 7 c2 I 7 c Maclaurin Series f0 f0I flZSO 272 fgfo 273 W I Examples 12 I3 x4 x3 I5 ex1x y1u forallx7 Sinxx7yi7 forallx7 12 x3 I4 12 x4 ln1xx77 7j 71lt27 17 cosx 7517 forallx Fourier Series If f is periodic with period 2 00 Trt 27rt m39rt ft alcos agcos ancos 2 p p I Trt 27rt m39rt blsin bgsm bnsm P P P Where P P P a0 3 ftdt an 1 ftcos quotit dt 71 0 12 3 ftsin quotit dt 17 p p p p p p p

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