MATH 151 SPRING 2010 COMMON EXAM I VERSION B 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 1 x2 5x 6 x 2 x2 x 6 1 Compute lim a 1 5 1 5 c 5 b d 1 e 0 3 4 x 5 2 Given f x 1 1 x if x 5 if x 5 which of the following statements is true when x 5 if x 5 a f is not continuous but the limit exists b f is continuous only from the left c None of the other statements is true d f is continuous only from the right e f is continuous 3 Given x 4 f x 4 for 0 x 4 what is lim f x x 2 x a Not enough information to answer b 2 c 4 d 1 e 0 2 4 The graph of f x a x2 9 has a horizontal asymptote at which of the following values 1 4x2 1 9 1 1 3 3 c 3 3 1 d 4 1 1 e 2 2 b 5 The graph of f x a x2 9 has a vertical asymptote at which of the following values 1 4x2 1 9 1 1 3 3 c 3 3 1 d 4 1 1 e 2 2 b 6 Which statement is true about the equation x5 x2 2x 3 a It has a solution on 1 2 by the Squeeze Theorem b It has a solution on 0 1 by the Squeeze Theorem c It has a solution on 1 2 by the Intermediate Value Theorem d It has a solution on 0 1 by the Intermediate Value Theorem e It does not have a solution 3 7 Given the vectors a 4i j and b 3i 5j which of the following is a unit vector in the direction of a 2b 12 2 i j a 148 148 7 5 b i j 74 74 11 2 i c j 153 153 7 5 i j d 102 102 11 2 i j e 125 125 8 Given triangle ABC with vertices A 2 4 B 1 3 and C 2 5 find the cosine of angle C 11 a 170 6 b 85 10 c 200 56 d 580 17 e 290 4 9 lim x 3 x x 3 1 3 b 0 a c 1 d 3 e 10 The graph of f is shown below Which of the following is the graph of f a b c d e 5 11 Which of the following give parametric equations of the line which passes through the points 1 1 and 1 4 5 3 t t a r t 2 2 b r t 1 t 1 4t c r t 1 2t 1 3t d r t 1 3t 1 2t e r t 5 3t 5 2t 12 The graph of a function f passes through the point 2 4 The slope of the line through 2 4 and 2 h f 2 h is 5 3h h2 Find the equation of the line tangent to f at x 2 a y 5x 14 b y 3x 10 c y 15x 34 d y 2x 3 e y 7x 18 6 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 10 points Use the limit definition of the derivative to find the derivative of f x 7 3 2 x 14 Given the point P 4 2 and the line r t 1 t i 2 2t j a 4 points Does line pass through each of the following points Write Yes or No in the blank Do NOT abbreviate 1 2 2 4 1 2 2 0 b 4 points Let Q be one of the points above through which does pass Find the vector b which starts at Q and ends at P c 4 points Find a vector a which is orthogonal to d 5 points Find the distance from P to 8 15 10 points Compute lim x x2 1 5x 2 x 9 16 10 points A woman walks due west on a ship at 4 mph The ship is moving N 30 W 30 degrees west of north at 20 mph Find the speed of the woman relative to the water NOTE your final answer does not need to be simplified but all trigonometric expressions which can be evaluated must be 10 cx2 x K 17 10 points Find the values of c and K which make f x 3 x cx 2 continuous at x 3 11 if x 3 if x 3 if x 3 DO NOT WRITE BELOW Question Points Awarded Points 1 12 48 13 10 14 17 15 10 16 10 17 10 TOTAL 105 12
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