MATH 151, SPRING 2010COMMON EXAM I - VERSION BLAST 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. Foryour 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 workneatly and concisely and clearly indicate your fin al answer. You will b e graded not merely onthe 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:11. Compute limx→2x2− 5x + 6x2+ x − 6.(a) −15(b)15(c) −5(d) 1(e) 02. Given f (x) =4 −35x if x < 51 if x = 5−1 + x if x > 5, which of the following statements is true when 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 rig ht.(e) f is continuous.3. Given −x + 4 ≤ f(x) ≤4xfor 0 < x ≤ 4, what is limx→2f(x)?(a) Not enough information to answer(b) 2(c) 4(d) 1(e) 024. The graph of f(x) =x2− 91 − 4x2has a horizontal asymptote at which of the following values?(a) −19(b)13, −13(c) 3, −3(d) −14(e)12, −125. The graph of f(x) =x2− 91 − 4x2has a vertical asymptote at which of the following values?(a) −19(b)13, −13(c) 3, −3(d) −14(e)12, −126. 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.37. Given the vectors a = −4i + j a nd b = 3i + 5j, which of the following is a unit vector in thedirection of a + 2b?(a)−2√148i +12√148j(b)−5√74i +7√74j(c)2√153i +11√153j(d)−5√102i +7√102j(e)2√125i +11√125j8. Given triangle ABC with vertices A(−2, 4), B(1, 3), and C(2, 5), find the cosine of angle C.(a)11√170(b)6√85(c)10√200(d)56√580(e)17√29049. limx→−3−xx + 3=(a)13(b) 0(c) ∞(d) −13(e) −∞10. T he graph of f is shown below.Which of the following is the graph of f′?(a) (b) (c) ..(d) (e) ..511. Which of the following give parametric equations of the line which passes through the points(−1, 1) and (1, 4)?(a) r(t) =52+32t, t(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. T he graph of a function f passes through the point (2, −4). The slope of the line throug h (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 − 186PART II WORK OUTDirections: Present your solutions in the space provided. Show all your work neatly andconcisely and Box your final answer. You will be graded not merely on the fina l answer, but alsoon 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) =32 + x.714. Given the point P (4, −2) and the line ℓ : r(t) = (−1 + t)i + (2 + 2t)j:(a) (4 points) Does line ℓ pass through each of the following points? Write “Ye s” or “No” in theblank (Do NOT a bbreviate!).(−1, 2). .(1, 2). .(2, 4). . (−2, 0). .(b) (4 points) Let Q be one of the points above through which ℓ does pass. Find the vector bwhich starts at Q and ends at P .(c) (4 points) Find a vector a which is orthogonal to ℓ.(d) (5 points) Find the distance from P to ℓ.815. (10 points) Compute limx→∞1√x2− 5x + 2 − x.916. (10 points) A woman walks due west on a ship at 4 mph. The ship is moving N30◦W (30 degreeswest of north) at 20 mph. Find the speed of the woman relative to the water. (NOTE: your finalanswer does not need to be simplified, but all trigonometric expr essions which can be evaluatedmust be).1017. (10 points) Find the values of c and K w hich make f(x) =cx2− x if x < 3K if x = 3x3− cx − 2 if x > 3continuous at x = 3.11DO NOT WRITE BELOW!Question Points Awarded Points1-12 4813 1014 1715 1016 1017 10TOTAL
View Full Document
Unlocking...