MATH 151 FALL 2010 COMMON EXAM I 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 10 mark the correct choice on your ScanTron using a No 2 pencil The scantrons will not be returned therefore for your own records also record your choices on your exam 3 In Part 2 Problems 11 16 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 number 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 10 40 11 10 12 6 13 10 14 10 15 10 16 14 100 1 PART I Multiple Choice 1 4 pts Find the vector a that has magnitude a 12 and makes an angle of 300 with the positive x axis a 6 6 3 b 6 3 6 c 6 6 3 d 6 3 6 e 6 3 6 6t2 3t t 3 t 2t 4 2 4 pts lim a 3 b 0 c 6 d 6 e 3 3 4 pts Find all vertical asymptotes for f x x2 1 x3 x2 a x 0 b x 1 x 1 c x 0 x 1 d x 1 e x 0 x 1 2 4 4 pts A force F 2 i 6 j moves an object from the point P 1 3 to the point Q 3 7 How much work is done if the force is measured in pounds and the distance is measured in feet a 19 foot pounds b 28 foot pounds c 68 foot pounds d 45 foot pounds e 32 foot pounds 5 4 pts Find the equation of the tangent line to the graph of f x x at x 1 1 2x 1 1 x 1 3 9 1 2 y x 1 3 9 1 4 y x 1 3 9 1 y x 1 9 1 1 y x 1 3 9 a y b c d e 6 4 pts The parametric equations x 3 sin t y 2 cos t describe a A circle b A parabola c An ellipse with major axis 3 and minor axis 2 d A line e A hyperbola 3 7 4 pts Find the value of a and b that makes f x x a bx2 3 if x 1 continuous and differentiable at x 1 if x 1 5 3 and b 2 2 1 9 a and b 2 2 a 0 and b 4 5 1 a and b 2 2 1 7 a and b 2 2 a a b c d e 8 4 pts What is the slope of the line that passes through the point 4 7 and is perpendicular to the vector h 5 6i a 4 7 5 6 6 c 5 7 d 4 b e 6 5 9 4 pts Which of the following intervals contains a solution to the equation x3 2x 2 7 a 1 2 b 2 1 c 1 0 d 0 1 e 2 3 10 4 pts If ABC is an equilateral triangle with sides of length 2 compute BA BC a 4 3 b 2 c 1 d 4 e 2 3 4 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 11 10 pts Find the distance from the point 1 7 to the line y 2x 3 5 12 6 pts Find the coordinates of the intersection point of the lines L1 and L2 given below L1 x 1 2t y 2 t L2 x 15 3w y 3 6w 6 13 For each of the following limits either calculate the limit if it exists or else explain why the limit does not exist i 4 pts lim x 0 ii 4 pts lim x 0 x2 2x x x2 2x x x2 2x x 0 x iii 2 pts lim 7 14 10 pts Using the definition of the derivative find f x for f x 8 4 x 1 15 10 pts The horizontal line through the point 3 1 is tangent to the parabola y x2 1 We see from the figure below that there is a second line tangent to the parabola at a a2 1 that also passes through the point 3 1 Find the value of a 9 x 3x 2 16 a 8 pts Find lim x 2 x2 4 x2 ax a 5 exists If so find the value of a If not explain x 3 x2 2x 15 b 6 pts Is there a value of a for which lim why End of Exam 10
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