M408Cmakeup2_sol - Mata/u. Exam ‘2. ath 408C Name Fall...

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Unformatted text preview: Mata/u. Exam ‘2. ath 408C Name Fall 2008 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. 4.143 + l 1. (14 points) Find all horizontal asymptotes of ftr) : {17‘ — 9(14 't)Ltf() (ii—1 _. cm s e, .1: : p .17 —t— 1 local extrema. Identify intervals on which f is increasing and those on which f is > . I"ind all critical numbers of f and classify the decreasing. 3. (l4 points) The concentration (7' of a certain chemical in the bloodstream 7‘ hours . . . . . . . -, 3t after injection into muscle tissue is given by ( (7‘) : M. +18. When is the conceir ) I. tration the greatest during the first 1 hours after the injection? (Verify that your solution corresponds to the absolute n aximum.) 4. (l6 points) Let = cos .1‘ w 2.2‘ for H g .r S 277. Sketch the graph of the curve y : clearly identifying any local extrema and inflection points that exist. You do not need to find the 1‘ intercepts. 5. (14 points) A particle moves along a coordinate line with acceleration alt) : l — 5 sin /. If the initial velocity of the particle is It units per second and the initial position is at the origin, where is the particle after 27 seconds have passed? 6. (14 points) A 25 foot ladder is leaning against a wall. The base of the ladder is pulled away from the wall at a constant rate of 2 feet per second. How fast is the angle between the ladder and the wall changing at the moment when the base of the ladder is l5 feet from the wall? ,_ i. (ll points) Use l subintervals to lmd upper and lower bounds for the area of / the region under the curve 3/ : lti — la 2. t) x. .1' fl 2. 2 (b) Express / 16 — 417261.17 as the limit of a Riemann sum (do not evaluate). 0 Bonus: (5 points) Right circular cylindrical cans are to be manufactured to contain a given volume. There is no waste m'.'ol\'ed in cutting the material for the vertical sides of the can. but each end piece is to be cut from a square and the corners are wasted. Find the ratio of height to diameter for the most economical cans. “ [/‘txbfl _,_ M U ‘(Y'H Xé%£ —- _ 3X3'L’ )( 70° 3y3'4 t £13.; V RAPHLH) 2 M V ‘Hfl/x’ _ V77; z 3AA: Y4” 5‘”/x: ‘ ’3? b /3 M M V‘fx‘H in _V_L( ya,” (3’: ’__‘_ —: x5 ‘t‘X-II) X ’4) (Y3 Y‘q’“ 3 ~‘Vx3 (hwux<v) 1: M -\)‘++\/ y—‘a_oo x; " fl ——3' 5~$gb 3 b 3 50%” 2W WM“ ‘(szsaw/ 3:473 1 -. ’ § _. WK): ;{%>(x%§g) = a (\MHM : 9(X4) (Y+Y) (K+03 .(I/y):o WM X: M f//I<)01M€ W Yz—I (m4~4owh-LA+L) c'Ie) we W t: -(mt'J bu} Hm ram To M w l3 OA‘ ¢ WM/W I t:z_l M UM C(0)/C(Z)lo—JC(‘€)'. CUM xslf) 0039=§0f=3 =5 w 9 cf a 7.}; (c) , 0W 2. 5* I a” 3 {r T; 3 "EM/5”“ ?‘ IR): IG~¥XL DEX-é L L: §£HJ+§¥Obrifif£3 AK 1»; 15%) g‘ =:(lc—4ta>) +£(IG‘4B‘F , L :(m-¥@f)+é(MJU =§(m+lz+¥+03:9«n- L ...
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M408Cmakeup2_sol - Mata/u. Exam ‘2. ath 408C Name Fall...

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