Math 132 Spring 2003 Exam 2 Name No calculators with a CAS are allowed Be sure your calculator is set for radians not degrees if you do any calculus computations with trig functions Part I Multiple Choice 5 points problem blacken your answers on the answer card 1 Find the value of B B B A F B C D G H 2 I 2e E diverges to J diverges to 2 For a certain radioactive isotope the amount remaining after 3 hours is 78 of the original amount What is its half life Round your answer to 2 decimal places A 6 21 hrs B 8 37 hrs C 8 85 hrs D 9 12 hrs E 9 24 hrs F 9 56 hrs G 9 75 hrs H 9 93 hrs I 10 12 hrs J 10 35 hrs 3 Suppose we perform the partial fraction decomposition B B B B B E B F B G B What is the value of F A F E F I F B F F F J F C F G F D F H F 4 During Lab 2 LoggerPro software collected the following data for time in sec and velocity in m sec Use Simpson s Rule to estimate the change in position displacement of the moving person for Round your answer to 2 decimal places A m E 0 13 m I m B m F m J 22 m C m G m D m H m 5 Find the value of B B A 17 08 F B if the integral converges B 19 03 C D G H I E diverges to J diverges to 6 Suppose a radioactive isotope is emitting radiation at a rate of millirems min beginning at time What is the total amount of radiation it will emit over all time that is if the process continues forever A millirems E millirems I 40 millirems B millirems C millirems F millirems G millirems J an infinite amount D millirems H 10 millirems 7 You use Simpson s rule with 8 to estimate the value of B B Using the error control formula we get ERROR l B B W l Find the best possible answer with this information round your answer to 6 decimal places A 0 000013 B 0 000042 C 0 000067 D 0 000093 E 0 000131 F 0 000147 G 0 000158 H 0 000169 I 0 000176 J 0 000187 8 According to one simple physiological model an adult male athlete needs 20 calories per day per pound of body weight to maintain his weight If he consumes more or fewer calories than those required to maintain his weight his weight changes at a rate proportional to the difference between the number of calories consumed and the number needed to maintain his current weight If an athlete weighs 160 lbs and consumes 3000 calories day which differential equation describes the athlete s weight at time In each equation k is a constant A 5 3000 B 5 C 29 5 D 5 150 8 E 5 3000 F 5 G 5 3000 H J 5 3000 160 I 5 160 9 Find the area in the first quadrant bounded by the curves C ln B C B and B 2 A 4 ln B ln F ln G ln ln C 1 D H 2 ln I 2 ln E J ln 10 Find W the Simpson approximation with 4 subdivisions for B B B A B C D E F G H I J 11 Suppose the velocity m sec of a point moving along a line satisfies 1 What is the position of the particle when A m F 27 m B m G 22 m C m H 17 m D m I 12 m E 35 m J 8 m 12 The temperature X of a body C at time min is changing at a rate of X X The slope field direction field for the differential equation is shown below Over the time interval which of the following are true you may need to use either the slope field or the differential equation itself to answer i If the temperature is 3 when then the body is cooler when ii No matter what the temperature is when the body is cooler after time iii The temperature of the body at time depends only on not on the initial temperature X of the body iv If the initial temperature of the body is 1 then the body never changes temperature A only i B only ii C only iii D only iv E only i ii F only i iii G only i iv H only ii iii I only ii iv J only iii iv 13 Using Euler s method with stepsize 2 B estimate C 0 5 if C B BC C C Round your answer to 2 decimal places The slope field pictured below is not needed for solving the problem but if you understand it it will help you narrow down your choices A 1 0202 F 0 3222 B 1 0465 G 0 2212 C 1 0625 H 2 0212 D 1 0842 I 2 0432 E 0 4322 J 2 4024 14 Suppose that B 0 w B B and that 0 w What is the value of 0 ww B ln B B Hint integration by parts A F B C G 2 H D I 3 E 1 J Part II True or False 1 point each Blacken your answers on the answer card 15 In Lab 2 you used a motion detector to gather position and velocity data When you backed away from the sensor LoggerPro recorded negative velocities A True B False 16 We can conclude that integral B B B B diverges by comparing it to the B A True B False A 17 Let A 0 be a solution of the differential equation A Then 0 0 A True 18 5 B False converges if and only if 5 A True B False 19 Let C be the amount of a radioactive isotope present at time If the isotope has halflife of 0 39 years then rounded to 2 decimal places C 1 78 C A True B False Part III These are two free response problems 20 21 worth a total of 25 points Write your answers on the test pages Show your work neatly and cross out irrelevant scratchwork false starts etc Please put your name on each of the following pages since they may be separated during grading Also please add your Discussion Section Letter available on your exam front cover sheet on each page so that we can return papers through discussion sections Name Discussion Section Letter 20 Note there may be several ways to do some of these integrals some harder some easier If you need the antiderivative of a function show how you got it a Find sin B cos B B b Evaluate B B Continued on other side B c Find B B B Name Discussion Section Letter 21 A tank …
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