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# ENGINEERING MATH I MATH 151

Texas A&M

GPA 3.92

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This 10 page Class Notes was uploaded by Evert Christiansen on Wednesday October 21, 2015. The Class Notes belongs to MATH 151 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/226044/math-151-texas-a-m-university in Mathematics (M) at Texas A&M University.

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Date Created: 10/21/15

PART 1 MULTIPLECHOICE PROBLEMS Each problem is worth 4 points NO partial credit will be given Calculators may NOT be used on this part ScanTrzm forms will be collected after 1 hour 1 E0 CA3 tancos1 2 a 2 b g c xP 1 d E 2 e E lim 1H0 a 2 b 2 c g ln1z 71 7 12 d 7 e 1 isin712z dz 2 a m b 2 lt gt m 2 C 7 I4 412 a 735214 e L 1274 41f f z4z2f 01 and f073then f3 5 533 a 0 b 9 C 16 d 24 e 27 The table gives the values of a function obtained from an experiment 00 1 0 2 Find the Riemann sum for A dz using four equal subintervals With right endpoints 0 5 1 0 0 5 1 5 0 2 2 0 01 Lil a 040 b 090 c 100 d 105 e 110 Evaluate lim 1 31COtz a 1n2 b e2 c e3 d e4 e 1 7 Which statement describes 13 7 312 7 9 to a f has a critical value at z 3 b f is increasing on 072 c f has a relative minimum at z 0 d f has a relative minimum at z 2 e f is concave upward on 071 Find the minimum value of z 2y given that my 50 and z and y are positive a 10 b 15 c 20 d 25 e 30 l l l i If 0 fzdz7 and 0 gzdz2then 0 fz74gzdz a 0 b 1 c 71 d 2 e 72 10 If Fz ASlnI dt then F 7r3 16 a g b 1 8V3 W 8 d g e 2 C 11 If then y a ICOSI ln 1 sin I 0081 I b 10051 7 In 1 Sin I 005x 1 C If sin I d 7 sinzcos 1008 I 71 e ICOSI 1nzsinz PART 2 WORKOUT PROBLEMS Each problem is worth 8 points Detailed analytic solutions must be provided Partial credit is possible Calculators are permitted ONLY AFTER the ScarLTrorLs are collected 12 A colony of bacteria grows at a rate proportional to its size The initial population is 108 l At the end of 10 minutes the population has increased to 103 X 10 l a Find the value of the proportionality constant kl 4 points b How long in minutes does it take the population to double its size 4 points 13 Find the absolute global maximum value of 91 13 7 312 7 91 on 72 4 i 14 Find the derivative of 721 tan71lnz 1 1 15 Let 91 114 7 616 i a Find the regions Where 91 is increasing or decreasing Clearly justify your answer 4 points b Find the regions Where 91 is concave up or concave downi Clearly justify your answer 4 points 16 Evaluate the following integrals Clearly show your reasoning ln 9 a ex dz 4 points ln 2 5 b 2 I 1 dz 4 points 17 A box With an open top is to be constructed from a square piece of cardboard7 6 ft Wide7 by cutting out a square from each of the four corners and bending up the sides Find the largest volume that such a box can have 18 A car braked With a constant deceleration of 36 ftsec27 producing skid marks measuring 1125 ft before coming to a stop How fast in feet per second was the car traveling When the brakes were rst applied

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