MATH 151, SPRING 2010COMMON EXAM I - VERSION ALAST 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 final answer. You will be 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+ x − 6x2− 5x + 6.(a) −15(b)15(c) −5(d) 1(e) 02. Given f (x) =4 −35x if x < 54 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 co ntinuous only from the left.(c) None of the other statements is true.(d) f is co ntinuous only from the right.(e) f is continuous.3. Given −13x + 2 ≤ f(x) ≤3xfor 0 < x ≤ 6, what is limx→3f(x)?(a) Not enough information to answer.(b) 2(c)12(d) 1(e) 024. The graph of f(x) =x2− 41 − 9x2has a ho rizontal asymptote at which of the following va lues?(a) −19(b)13, −13(c) 2, −2(d) −14(e)12, −125. The graph of f(x) =x2− 41 − 9x2has a vertical asymptote at which of the following values?(a) −19(b)13, −13(c) 2, −2(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 2a + b?(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 A.(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. The graph of f is shown be low.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 p oints(−1, 1) and (2, 3)?(a) r(t) =53+23t, 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 − 2t, 5 + 3t >12. The g raph 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 3 + 5h + h2. Find the equation of the line tangent to f at x = 2.(a) y = 5x − 14(b) y = 3x − 10(c) y = 17x − 38(d) y = 2x + 5(e) y = 9x − 226PART 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 final answer, but alsoon the quality and c orrectness of the work leading up to it.13. (10 points) Use the limit definition of the derivative to find the derivative of f (x) =23 + x.714. Given the point P (−1, 2) and the line ℓ : r(t) = (1 + 4t)i + (2 − 2t)j:(a) (4 points) Does line ℓ pass through each of the following points? Write “Yes” or “No” in theblank (Do NOT abbre viate!).(1, 2). .(4, −2). .(−2, −1). . (5, 0). .(b) (4 points) Let Q b e 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− 3x + 2 − x.916. (10 points) A woman walks due west on a ship at 4 mph. The ship is moving N 30◦W (30 deg reeswest of north) at 20 mph. Find the spee d of the woman relative to the water. (NOTE: your fina lanswer do e s not need to be simplified, but all trig onometric expressions which can be evaluatedmust b e ).1017. (10 points) Find the values of c and K which make f (x) =cx2+ 4x if x < 3K if x = 3x3+ cx + 1 if x > 3continuo us at x = 3.11DO NOT WRITE BELOW!QuestionPoints Awarded Points1-12 4813 1014 1715 1016 1017 10TOTAL
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