Math 132 Spring 2003 Exam 4 Final Exam Name ID Number 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 1 17 Multiple Choice 5 points problem mark your answers on the answer card 1 What is the volume of the solid that results from revolving around the B axis the region in the first quadrant under C cos B and above B 1 A B F 1 G C 1 H 21 D 1 E 2 I 3 J 1 2 A spring is stretched beyond its natural length A meter is used to measure the force lbs needed when the spring has been stretched B ft Some of the data collected is B ft 0 1 force lbs 0 How much work is done in stretching the spring 6 ft beyond its natural length A 9 ft lbs B 10 5 ft lbs C 45 5 ft lbs D 18 ft lbs E 4 ft lbs F 5 5 ft lbs G 7 5 ft lbs H 22 ft lbs I 32 ft lbs J impossible to determine since there s no formula for the force J B acting at B 3 The area in the first quadrant between the curves C B and C B and above the interval is given by which of the following A C B B E B B B B B B B B B D B B B B F B B B B B B 4 Find the value of A F B ln B B if the integral converges B 1 C D E G H 5 429 I 3 879 J integral diverges 5 If C satisfies the differential equation C w A 0 B F G 2 B C B and C what is C C 2 D H 3 I E J 3 6 Which differential equation listed could have the direction field pictured below A C w E C w C B C B B C w B C C w B C D C w BC C F C w B C G C w C B H C w C C 8 7 What is the radius of convergence of the power series 8 x 8x B 8 A 0 F B G 2 C H 3 D I 4 E 1 J 8 Under a specially negotiated contract a bank has agreed that for 20 years the amount of money in my account will grow at a rate of 100 yr starting at time years How much does my account change in value over the first 5 years Round your answer to the nearest cent A 115 93 B 145 51 C 237 63 D 254 65 E 317 98 F 319 78 G 539 45 H 552 38 I 642 31 J 643 97 9 The function 0 B B cos B has a series representation valid for all B 0 B B B 8 B8 What is the coefficient in that series A 0 F x B G x C 1 H x D x I E x x J 2 10 A random variable has the probability density function 0 B What is the value of B0 B B B B B A B C D F 0 1 G 0 001 H 0 000001 I 10 E J 10 11 For the random variable in Problem 10 what is T Round your answer to 4 decimal places A 0 4431 B 0 6321 C 0 1178 D 0 1198 E 0 7739 F 0 4317 G 0 5529 H 0 0021 I 0 9112 J 0 1267 12 An experimenter begins with 10g of a radioactive substance After 1 year of decay only 1 g of the material remains If C denotes the number of grams present at time what is the relative rate of decay 5 in the differential equation C 5C A F ln ln ln 10 B 10 C ln 10 D ln E G ln H ln I ln J 5 half life of the substance 13 A particle moves along a straight line path with acceleration Between times and its displacement is At its velocity is What is the value of Hint integration by parts A B C D E F G H I J 6 14 Let 0 B B B B for those B s for which the series converges If we use B B B as an approximation to 0 B on the interval then we know that the absolute error l0 B B B B l Pick the best answer below round your answer to 3 decimal places A 132 B 0 112 C 0 119 D 0 127 E 0 012 F 0 001 G 0 002 H 0 003 I 0 005 J 0 006 15 For the function 0 B in Problem 14 find 0 A F B G C H D I E J 16 The power series 8 ln88 B 8 has radius of convergence 1 What is the 8 interval of convergence A B C D E F G H 17 If C C C what is A F B 1 G C H D E I J Part II 18 27 True False 1 5 points problem mark your answers on the answer card The functions L B constant G B A True and O B B differ by some B False 19 If we write sin B B 1 B 1 B 1 then coefficient A True B False 8 20 The series 8 8 converges because lim 8 8 8 8 8 A True 21 x A True B False x x x B False 22 We can conclude that B B diverges by comparing it to the integral B B A True B False 23 The series converges 8 8 A True B False 24 The series 8 B8 and 8 B 8 have the same radius of convergence The 8 s 8 8 are the same in both series A True B False 25 Suppose C 0 B for B Simpson s Rule approximates the area under the graph of 0 B and above by using trapezoids A True B False 8 26 The series sin 8 converges absolutely and therefore converges 8 A True B False 27 We can conclude that the series convergent series 8 8 8 8 lsin 8l 8 A True B False converges by comparing it to the
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