MATH 151 SPRING 2011 COMMON EXAM III VERSION A LAST NAME First name print INSTRUCTOR SECTION NUMBER UIN SEAT NUMBER DIRECTIONS 1 The use of a calculator laptop or computer is prohibited 2 In Part 1 Problems 1 12 mark the correct choice on your ScanTron using a No 2 pencil For your own records also record your choices on your exam 3 In Part 2 Problems 13 17 present your solutions in the space provided Show all your work neatly and concisely and clearly indicate your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 4 Be sure to write your name section and version letter of the exam on the ScanTron form THE AGGIE CODE OF HONOR An Aggie does not lie cheat or steal or tolerate those who do Signature DO NOT WRITE BELOW Question Points Awarded Points 1 12 48 13 12 14 15 15 8 16 9 17 8 TOTAL 100 1 ex cos x 2x x 0 x2 2x 1 Find the limit lim a 1 b 1 2 c 0 1 d 2 e Limit does not exist 2 Solve the equation ln x ln x 1 ln x 4 for x a x 0 and x 3 b x 4 only c x 2 and x 2 d x 3 only e x 2 only 3 Which graph of f below has the property that the derivative f is always positive and decreasing e None of these graphs 2 For questions 4 5 the graph of the FIRST DERIVATIVE of a function f is shown below 4 On which interval s is the ORIGINAL FUNCTION f decreasing a b d b a c e c c d b d e None of these 5 At what value s of x does the ORIGINAL FUNCTION f have a local minimum a x a x c and x e b x c only c x a and x e d x b only e x b and x d 6 Find the value of log4 1 8 1 32 2 3 1 2 2 3 2 a b c d e 3 7 A bacteria culture starts with 200 bacteria and triples in size every half hour Assuming exponential growth how many bacteria are there after 45 minutes ignore any appropriate rounding a 600 3 b 750 c 400 2 d 1200 ln 3 2 e 800 ln 3 8 Find the value of cos tan 1 4 1 a 17 4 b 17 1 c 15 4 d 15 15 e 4 9 Find the absolute maximum and absolute minimum values of the function f x x3 3x 1 on the interval 1 3 a minimum value 4 maximum value 20 b minimum value 1 maximum value 3 c minimum value 1 maximum value 19 d minimum value 3 maximum value 19 e minimum value 8 maximum value 10 4 10 Which of the following is an antiderivative of f x ln x 1 ln x 2 2 b ex 1 c x d x ln x x a e x ln x x f x h f x h 0 h 11 If f x 5x what is lim a x5x 1 b ln 5 5x c Does not exist d 5x 5x e x 2 12 The acceleration of a car is given by a t 3t 2 in ft sec If the car is at rest at time t 0 what is the car s velocity when t 2 13 ft sec 4 b 8 ft sec a c 12 ft sec 9 d ft sec 2 e 10 ft sec 5 PART II WORK OUT Directions Present your solutions in the space provided Show all your work neatly and concisely and Box your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 13 6 points each a Find and simplify the derivative of f x x arctan x b If g x ln 3x 2 e4x find g 0 6 1 ln 1 x2 2 14 The derivative of a function f is given by f x x 2 e3x a 4 points Find the intervals where the original function f is increasing or decreasing b 3 points List and classify as max or min the x coordinates of all local extrema of the original function f c 8 points Find the intervals where the original function f is concave upward or concave downward 7 15 8 points A rectangular container with no top and a square bottom is to have a volume of 8 ft3 Material for the sides costs 1 per ft2 and material for the bottom costs 4 per ft2 Find the dimensions that will minimize the cost of the container Clearly show that your answer is indeed a minimum 8 is shown 16 9 points The region that lies under the graph of f x cos2 x from x 0 to x 3 below a Using sigma notation write an expression to n approximate the area under the graph of o y f x with rectangles using a partition P 0 with x i being the right endpoint 4 3 of each subinterval b Evaluate the rectangle area expression in part a Your answer does not have to be simplified but all trig expressions which can be evaluated must be c On the graph above sketch the approximating rectangles 9 2 17 8 points Find the limit lim cos x 1 x x 0 10
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