MATH 151, FALL 2010COMMON EXAM I - VERSION ALAST NAME, First name (print):INSTRUCTOR:SECTION NUMBER:UIN:SEAT NUMBER:DIRECTIONS:1. The use of a calculator, laptop or c omputer is prohibited.2. In Part 1 (Problems 1-10), mark the correct choice on your ScanTron using a No. 2 pencil. The scantrons will notbe 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 conciselyand clearly indicate your final answer. You will be graded not merely on the final answer, but also on the qualityand 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 HO NOR“An Aggie does not lie, cheat or steal, or tolerate those who do.”Signature:DO NOT WRITE BELOW!QuestionPoints Awarded Points1-10 4011 1012 613 1014 1015 1016 141001PART I: Multiple Choice1. (4 pts) Find the vector ~a that has magnitude |~a| = 12 and makes an a ngle of 300◦with the p ositive x-axis.(a)6, 6√3(b)6√3, 6(c)6, −6√3(d)6√3, −6(e)−6√3, −62. (4 pts) limt→∞6t2+ 3t(3 − t)(2t + 4)=(a) 3(b) 0(c) 6(d) −6(e) −33. (4 pts) Find all vertical asymptotes for f (x) =x2− 1x3+ x2.(a) x = 0(b) x = 1, x = −1(c) x = 0, x = 1(d) x = 1(e) x = 0, x = −124. (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 ifthe force is measured in po unds 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 pounds5. (4 pts) Find the equation of the tange nt line to the graph of f (x) =x1 + 2xat x = 1.(a) y −13= −19(x − 1)(b) y −23=19(x − 1)(c) y −13= −49(x − 1)(d) y =19(x − 1)(e) y −13=19(x − 1)6. (4 pts) The parametric equations x = 3 + s in t, y = −2 + cos t describe(a) A circ le(b) A parabola(c) An ellipse with major ax is 3 and minor axis 2(d) A line(e) A hyperbola37. (4 pts) Find the value of a and b that makes f (x) =−x + a if x ≤ 1bx2+ 3 if x > 1continuous and differentiable at x = 1.(a) a =52and b = −32(b) a =92and b =12(c) a = 0 and b = −4(d) a =52and b = −12(e) a =72and b = −128. (4 pts) What is the slope of the line that pas ses through the point (4, 7) and is perpendicular to the vector h−5, 6i?(a) −47(b)56(c)65(d)74(e) −659. (4 pts) Which of the fo llowing intervals contains a solution to the eq uation 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 equila teral tr iangle with sides of length 2, compute−−→BA ·−−→BC.(a) 4√3(b) 2(c) 1(d) 4(e) 2√34PART II WORK OUTDirections: Present your solutions in the space provided. Show all your work neatly and concisely and Box yourfinal answer. You will be graded not merely on the final answer, but also on the quality and correctness of the workleading up to it.11. (10 pts) Find the distance from the point (1, 7) to the line y = 2x + 3.512. (6 pts) Find the coordinates of the intersection point of the lines L1 and L2 given below.L1: x = −1 − 2t, y = 2 + tL2: x = 15 − 3w, y = 3 + 6w613. For each of the following limits, either calculate the limit, if it e xists, or else explain why the limit does not exist.(i) (4 pts) limx→0+x2+ 2x|x|(ii) (4 pts) limx→0−x2+ 2x|x|(iii) (2 pts) limx→0x2+ 2x|x|714. (10 pts) Using the definition of the derivative, find f′(x) for f (x) =4x + 1.815. (10 pts) The horizontal line through the point (3, 1) is tangent to the parabola y = x2+ 1. We see from the figurebelow that there is a second line tangent to the parabola at (a, a2+ 1) that als o passes through the point (3, 1).Find the value of a.916. (a) (8 pts) Find limx→2x −√3x − 2x2− 4(b) (6 pts) Is there a value of a for which limx→−3x2+ ax + a + 5x2− 2x − 15exists? If so , find the value of a. If not, ex plainwhy.End of
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