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# 410 Note for MA 22200 at Purdue

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

MA 222 Final Exam Practice Problems The Formula Page may be used It will be attached to the nal exam 1 10 11 12 13 Find f7r2 if m A 727139 B 747139 C 27139 D 7139 E 7T8 dy Ify lnsec17 then A cosa B lnsecatanr Csin1 D tana E seca Express as a single logarithm 11113 7 ln A mo3 7 B may 0 ln16 D 1143 g E 1mg If y 902 calculate 3 2 2 2 A 2176QC B e200 C 3726 1 D 2262QC E e If y ln vat 1 calculate 3 217 a 1 A B D V372 1 V372 1 2at2 1 Find an equation for the tangent line to the curve 61 m2 2 at the point 17 0 Ayr71 By2172 Cy72172 Dy7171 Ey721772 E None of these 39m21 Find the maximum value of the function fl m21n2r A 1 B e2 C 26 D 2 E 26 Which of the following best describes the function y Ina 7 17 A There is a relative minimum at a 1 and the curve is concave down for all a gt 0 B There is a relative maximum at a 1 and the curve is concave down for all a gt 0 C There is a relative maximum at a 17 the curve is concave down for 0 lt a lt 17 and concave up for a gt 1 D There is a relative minimum at a 17 the curve is concave down for 0 lt a lt 17 and concave up for a gt 1 E None of these The velocity of an object falling through a resisting medium is given by v 1001 7 67000 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 rcos 217 A 71 sin 217 cos 217 B 7217 sin 217 cos 217 C a sin 217 cos 21 D 21 sin 217 cos 21 E 72 sin 217 cos 21 Evaluate V1737 AIlnl17r2 C B 217E2C C7lnl17v2C D717172C ENoneof these 3 1 Evaluate da 17 2 A61nlv5llnlr1l0 B31nr2lnlrlC C31nlr2alC Dlnlrl7lnlr1lC E lnlm2llnla 1l0 3 Evaluate ln rdat Give your answer correct to 2 decimal places 1 A 194 B 150 C 7021 D 101 E 127 MA 222 14 15 16 17 18 19 20 21 22 23 Final Exam Practice Problems Find the area of the region bounded by the graph of y sin 217 the 17 aXis7 and the lines a 0 and a I 2 A2B1C0D1E 2 4 Find the rst three non zero terms of the Maclaurin series of fl V1 317 A fx1ga7 a2 B fr1x13a7713a7 c fr1r7 r2 D at 1 gx1 31 7 31 33 E fa 1 g 7 312 Using the Maclaurin series ln1 a a 7 I2 173 7 in 175 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 fl sin 21 in powers of 1 7 Af l77721Bf277 72 7 5 0 f0 7 7 0 7 33 0 7 35 13 f0 751 v 7 g 7 10 7 321 E None of these 03 Approximate cos Vida 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 for77T a lt0 1 for0 a 0 for ltzr 7r it calculate the rst three non zero terms of the Fourier series for That is7 the rst three non zero terms in the series 610 11 cos a In sina 12 cos 21 1 sin 217 A l cosrsinr B i cosr7 sinr C i7 5 it Tcoszrcos2r D Z cosr sinr E None of these Find the general solution of the differential equation y2da 17 12dy 0 1 1 A x13 y30 B 1CClnlat1llnlylC 1 D2r12yC Er7C y 1 Find the particular solution of the differential equation 3 7y 32 Where y 2 When a 1 a 174 7 173 5 173 7 173 7 A 7 7B 7 7C 7 7D 7 7EN fth y 44 y 33 y 44 y 44 oneo ese Find the particular solution of the differential equation y y 7 6y 0 Where 3 0 and y71Whenr0 A y 7126 3 362 B y 726300 36 C y D y 726300 6 2 E None of these 767300 6200 Find the general solution of the differential equation D23 7 Dy y 0 A y Cle1 g 2 Cgea V q W2 B y 6 C1 sin3I2 C2 cos3r2 C y 6 C1 sin3I C2 cos3r D y ex2C1 sin3r2 C2 cos3r2 2 MA 222 24 25 26 27 28 29 30 31 32 33 34 35 Final Exam Practice Problems E None of these Find the equation of the orthogonal trajectories of the curves y 0175 A 15cm3y1 BI25y2c Cy 15x3c Dlnlyllnla lc E5cy17471 Find the equation of the curve for Which the slope at any point 17 y is a y and Which passes through the point 07 1 Ay2e 71771 Byc a 2 Cy7 v1Dy2e 7v71 Eyc v An object moves With simple harmonic motion according to the equation 2730 641 0 Find the displacement at as a function oft if a 4 and 27 3 When t 0 A a 4sin8t 2cos8t B a 3sin8t 4cos 8t C a 67 sin64t 4cosG4t D a gsin8t 4cos 8t E a 8sin8t 4cos8t Find the general solution of the differential equation D23 8Dy 16y 0 A y C1lt3 4 C2Ie 4QC B y C16490C2z1764QC C y Cle 4 c26 4 C D y C1 sin 4mc2 cos 41 E y C164QC 0267400 Calculate the Laplace transform of 26 sin 4t 8 8 8 2 A B D E 373216 33216 373216 333216 33216 2 Calculate the inverse Laplace transform of 8 32 33 7 4 A 4e4t 7 ct B 464 6 C 0164 6 D 464 6 E None of these Calculate the Laplace transform of the expression y 7 33 2y7 Where y at f0 71 and fO 2 A 327332Lf B 32Lf372 C 327332Lf37 1 D 327332Lf3 1 E 32 7332Lf 375 Find the Laplace transform of the solution of the differential equation 3 2y 6 Mo 12 1 2 1 2 1 1 A 7 B 2 D 322 32 32322 3723722 3722 Use Laplace transforms to solve the differential equation y 9y 3t y0 17 y 0 71 A y it 7 gsin3t cos3t B y 5t 7 sin3t cos3t C y 4cos3t 7 sin3t D y cos3t 7 sin3t E None of these Use Laplace transforms to solve the differential equation D23 7 2Dy y 6 340 0730 0 A y 2t2et B y t26 t C y t2 t D y tZe t E y 2te t 3 If 3 3 7 Ms 2 B and C are constants Which of the following is the partial fraction expansion of f37 A7 A A B C B A B C A3 B3 C3 371 371 32 393712 32 371 3712 32 D A B C A B 39371 3712 32 39371 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 3 MA 222 Final Exam Practice Problems temperature to drop tp 15 C A 935 min B 125 min C 1434 min D 862 min E 1733 min 36 If the current in an AC circuit is given by i cost sin t then the rst maximum of the current after t 0 is 1 l A2ABWA C1A D AE A 37 A certain radioactive substance decays according to the law N 66 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 t When t 2 rounded to the nearest hundredth A 022 B 002 C 002 D 022 E 0012 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 A 14 B 15 E 16 C 17 A 18 B 19 D 20 B 21 C 22 A 23 D 24 B 25 D 26 D 27 A 28 B 29 B 30 E 31 C 32 A 33 C 34 D 35 C 36 D 37 A

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