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# Calculus For Technology II MA 22200

Purdue

GPA 3.97

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This 4 page Class Notes was uploaded by Dorothea Bode on Saturday September 19, 2015. The Class Notes belongs to MA 22200 at Purdue University taught by Staff in Fall. Since its upload, it has received 45 views. For similar materials see /class/208128/ma-22200-purdue-university in Mathematics (M) at Purdue University.

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Date Created: 09/19/15

MA 222 Final Exam Practice Problems The Formula Page may be used It will be attached to the nal exam Find f7r2 if m M a A 727139 B 747139 C 27139 D 7139 E 7T8 H 3 dy Ify 7 lnsec17 then 7 A cosa B lnsecatanr Csin1 D tana E seca 9 Express as a single logarithm 11113 7 ln A mo3 7 B may 0 ln16 D 1143 g E 1mg 4 If y 902 calculate 3 2 2 2 A 2176QC B e200 C 3726 1 D 2262QC E e 5 If y ln vat 1 calculate 3 1 217 a 1 A 7 B 7 C 7 D 7 E None of these 121 121 m21 2at21 6 Find an equation for the tangent line to the curve 61 m2 2 at the point 17 0 Ayr71 By2172 Cy72172 Dy7171 Ey721772 7 Find the maximum value of the function fc m21n2r A 1 B e2 C 26 D 2 E 26 8 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 9 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 10 Find 3 if y rcos 217 A 71 sin 217 cos 217 B 7217 sin 217 cos 217 C rsin 217 cos 21 D 21 sin 217 cos 21 E 72 sin 21 cos 21 rda 11 Evaluate 7 1 7 2 A atln l 1712 1 0 B 217E2C C7lnl17172 10 D 717E2C E Noneof these 3 1 12 Evaluate da 17 2 A 61nlm5llnla 1l0 B 31nr2lnlr C C 31nlm2ml0 D lnlzrl 7lnlm1lC E lnlm2llnla 1l0 3 13 Evaluate ln rdat Give your answer correct to 2 decimal places 1 A 194 B 150 C 7021 D 101 E 127 MA 222 Final Exam Practice Problems 14 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 15 Find the rst three non zero terms of the Maclaurin series of fl A fa 1 gx7 x2 B fa 1m7 13x c fr1r7 r2 D fl 1m7 13a E fl 1a 7 a 2 16 Using the Maclaurin series ln1 a a 7 1112 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 H l V Find the rst three non zero terms in the Taylor series for at sin 21 in powers of 1 7 A f0 lt 177 7 93 7 32 13 f0 2W7 7 2 7 32 037 35 0 f0 7 7 0 7 33 0 7 35 13 f0 g v7 g 7 i0 7 321 E None of these 001 H 00 03 Approximate cos dm using three terms of the appropriate Maclaurin series Give your answer correct to 4 decimal places A 08538 B 02779 C 09553 D7 02955 E 01863 H 33 If f is a periodic function of period 27139 and 0 for77rgatlt0 fl 1 for0 a 0 for ltai 7r calculate the rst three non zero terms of the Fourier series for That is7 the rst three non zero terms in the series a0 a1 cos a b1 sin a a2 cos 21 1 sin 217 A icosa sina B i cosr7 sina C i 7 gCOS cos2a D Z cosc sina E None of these 20 Find the general solution of the differential equation y2da 17 12dy 0 1 Am13y30 B CClnlm1llnlylC I1 1 D2r12yC Ex7C y 1 21 Find the particular solution of the differential equation 3 7y 32 Where y 2 When a 1 a 174 7 173 5 173 7 33 7 A 7 7B 7 7C 7 7D 7 7EN fth y 44 y 33m y 44m y 44 oneo ese 22 Find the particular solution of the differential equation y y 7 6y 0 Where y 0 and y71Whenr0 A y 726 390 362 B y 726300 36 C y 76 390 62 D y 756300 6 2 E None of these 23 Find the general solution of the differential equation D23 7 Dy y 0 A y Clel g 2 Cgea VEW2 B y 6 C1 sin I2 C2 cos r2 C y 6 C1 Sln il7 C2 COS I D y ex2C1 sinx r2 C2 cos r2 2 MA 222 2 q 2 UV 2 o 2 1 3 00 Find the Laplace transform of the solution of the differential equation 3 2y 6 If f3 Final Exam Practice Problems E None of these Find the equation of the orthogonal trajectories of the curves y c375 A 15cm3y1 BI25y2c Cy c D lnlyllnla lc E5cy17471 1533 Find the equation of the curve for Which the slope at any point 17 y is 37 y and Which passes through the point 071 Ay2e 7m71Byexa 2 Cy7v1Dy2e 7v71 Eye v An object moves With simple harmonic motion according to the equation 2730 641 0 Find the displacement mas afunction oftifat4and 27 3Whent0 Am4sin8tgcos8t Bv3sin8t4cos8t Cv6731sin64t4cos64t Dvgsin8t4cos8t Ev8sin8t4cos8t Find the general solution of the differential equation D23 SD 16y 0 A y C1lt3quotmc2176 4QC B y C164x0264x C y Cle 4mc26 49C D y c1 sin 4mc2 cos 41 E y c164QC 0267400 Calculate the Laplace transform of 26 sin 4t 8 2 A B C D E 373216 33216 373216 333216 33216 2 Calculate the inverse Laplace transform of 8 32 33 7 4 A le 7 ct B 4e 4t ct C le e t D 464 e t E None of these Calculate the Laplace transform of the expression y 7 33 2y7 Where y at f0 71 and fO2 A 327332Lf B 32Lf372 C 327332Lf371D 327332Lf31 E 327332Lf375 2t y012 1 2 1 2 1 1 A732 707 inf 7E7 322 32 32322 3723722 3722 Use Laplace transforms to solve the differential equation y 9y 3t y0 17 y 0 71 A y t7 gsin3tcos3t B y 7sin3tcos3t Cy4cos3t7sin3t D ycos3t7sin3t E None of these Use Laplace transforms to solve the differential equation D23 7 2Dy y ct 340 0730 0 A y 2t2et B y itZE t C y t2 t D y tZe t E y 2te t m which of the following is the partial fraction expansion of f37 A7 B and C are constants C Aijr 371 371 32 393712 32 371 3712 32 D iiL E ii 371 3712 32 371 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 If the current in an AC circuit is given by i cost sint then the rst maximum of the current after t 0 is 1 1 A2ABWA C1AD2AE A 3 1 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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