M408CF09_Makeup3_Sol - Exam 3 Math 408C Name Fall 2009 TA...

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Unformatted text preview: Exam 3 Math 408C Name Fall 2009 TA Discussion Time: TTH . You must show sufficient work in order to receive full credit for a problem. Do your work on the paper provided. Write your name on this sheet and turn it in with your work. Please write legibly and label the problems clearly. Circle your answers when appropriate. No calculators allowed. 1. (13 points) An object moves along a straight line. Its velocity at time t is given by v(t) = 3 — V2 + t, for 2 S t g 14. Find the total distance traveled by the object over this time interval. 2. Let R be the area of the region enclosed by curves y = x2, y = 2 — 1c and y = 0. (a) (13 points) Find the area of R. (b) (13 points) Find the volume of the solid generated when R is rotated about the y axis. dT 5t3 3. (13 points) The temperature an oven is changing at a rate of —— dt 154 + 1 per minute Where t 2 0 is measured in minutes and T is measured in degrees Celsius. What is the net change in the temperature in the oven over the first ten minutes? H degrees 4. (12 points) Solve for x: In 24 — lnx = ln(:r — 5) 5. (12 points) Let f (x) = (:17 + 2)? Find the slope of the tangent line to the curve y = f(m) when :r = 2. 6. Find the indefinite integrals (a) (12 points) / :rsec2 :rdx em (b) (12 points) / “6235 Bonus: (5 points) Prove the identity 251n_1(:c) = cos‘1(1 — 2x2) for all :r 2 0. dz: ’ U’H:\: 3- D+t ,Jstslq Tow oewwt- MW = j’Hw/Uaow 2. w _. L 3; 9- , - L311: - 3(J+t3] 4 L27§(a+e)3" .. at] l 7' 1‘ al— %(2?3 —(L-%’<8)) 4— 2730,43 - Vz-(Z(27)—2I\ = (cu—l, -4142.) +£60.14”) +4.4 ~24) M e w St} 0% wU=Lq~H . 6‘“ Mcqéfi (AA/«6:0, (4:! q wM-tria,u=/o+l 10H ‘ = “" "'"‘ JAN 4 U. I 4- MRH—JIMX - J/Mx'fl M(fi):J/h(x-’S’) ¥ 2"} ._———~ : -r Y X 94 : Yz'S‘V u .k 14 ...
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