MATH 151, FALL 2008COMMON EXAM II - 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 1-10), 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 11-16), present your solutions in the space provided. Show all your work neatly and conciselyand clearly indicate your final answer. Yo u 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 n umber 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 1212 1013 1014 815 1216 81001PART I: Multiple Choice1. (4 pts) Find the inverse function of f (x) =1 − x4x + 3(a) f−1(x) =4x + 31 − x(b) f−1(x) =3x − 14x + 1(c) f−1(x) =1 − 3x4x + 1(d) f−1(x) =3x − 14x(e) f−1(x) =1 − 3x4x2. (4 pts) Evaluate limx→0−e1/x(a) e(b) 1(c) −∞(d) ∞(e) 023. (4 pts) If Q(x) is the quadratic appr oximation for f (x) =2xat x = 1, then Q12=(a) 3(b)72(c)92(d)52(e)324. (4 pts) An object is moving with position function f (t) = 2 sin t−3 cos t. Find the velocity, v(t), and the acceleration,a(t), at t =π6.(a) vπ6=√3 −32aπ6= 1 −3√32(b) vπ6=√3 −√32aπ6= 1 −3√32(c) vπ6= −√3 −32aπ6= −1 +32(d) vπ6=√3 +32aπ6= −1 +3√32(e) vπ6= 1 +3√32aπ6= −√3 +3235. (4 pts) In order to solve the equation x5− 2x + 5 = 0, we apply Newton’s Method with an initial guess x1= 1.What value does Newton’s Method give for x2, the second approximation?(a)14(b)74(c) −14(d)73(e) −136. (4 pts) If g is the inverse of f , find g′(2) if it is known that f (3) = 2, f′(3) = 7, f (2) = 11 and f′(11) = 8. Assumeg to be differentiable.(a)18(b)12(c)17(d)111(e)1547. (4 pts) Solve the equation ln(x + e) + ln(x − e) = 2 + ln 3.(a) x = 2e only(b) x = 2e and x = −2e(c) x = 3e only(d) x = 1 and x = 3e(e) No solution8. (4 pts) Find the tange nt vector of unit length for r(t) =e2t, t cos tat t = 0.(a)2√5,1√5(b) h1, 1i(c) h1, 0i(d)1√2,1√2(e) h2, 1i59. (4 pts) If h(x) = f ◦ g = f (g(x)), find h′(−3) given that g′(−3) = 4, f′(−3) = 7, g(−3) = −2, f′(−2) = 11, andf′(4) = −3(a) −6(b) −14(c) 44(d) −3(e) 2810. (4 pts) limθ→0sin2(3θ)θ2=(a)13(b) 9(c)19(d) 3(e) The limit does not exist6PART II WORK OUTDirections: Pres e nt 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 fina l answer, but also on the quality and correctness of the workleading up to it.11. Find the derivative of:(i) (6 pts) f (x) = tan(2x3) + tan3(x)(ii) (6 pts) g(t) =p1 +√t.712. (10 pts) Water is poured into a conical cup at the rate of52cubic inches per se c ond. If the cup is 6 inches tall andthe to p of the cup has a radius of 2 inches, how fast do e s the water level rise when the water is 2 inches deep? Besure to include units with your answer. NOTE: The volume of a cone is V =13πr2h.813. (10 pts) Find the equation of the tangent line to the c urve y2sin 2x = 8 − 2y at the pointπ4, 2.914. Consider the curve given by parametric equations x = t3− 6t2, y = t2− 6t(i) (6 pts) Find the e quation of the tangent line at t = 1.(ii) (6 pts) Find all points on the curve where the tangent line is:(a) vertical(b) horizontalExam continues on next page1015. (8 pts) Use differentials or a linear a pproximation to approximate√9.02.16. (8 pts) Find all value(s) of x, 0 ≤ x ≤ 2π, where f (x) = x + 2 sin x has a horizontal tangent.End of
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