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M408CF08Makeup1Sol - Exam 1 Math 4080 Name Fall 2008 TA...

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Unformatted text preview: Exam 1 Math 4080 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 lame 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. Calculate the limits below, if they exrst. In the case that a limit doesn’t exist. indicate whether the limit approaches >c. —DC. or neither. You must show sufficient work to get credit for a correct answer 1 21* (a) (10 points) lim ( _ > T—"Z J7 _ '_) (1.2 _ 4 - l i 10"'t' 1' [(1-4) (3)( porn s) hp}; l 2‘ I22 . . 2 — m (C) (10 pomts) Egg—W— 2. (l0 points) Find a value of c such that the function f below is continuous every- where. :1'2 + 2.1~ — .3 .L‘ — l 7 \/c;r+3, :1? 21 3. (10 points) Use the definition of dcriyatiye to calculate f’(0) for f(.r) : .r (l ft?) : .) ‘ - .r‘ -i- I, (You must use the definition. not the diflcrcntiahon rules. in order to get credit tor this problem.) 4. (10 points) An object moves along the y—axis. its position at time 1‘, given by , _ t2 . . . . y(/;) : +— for 0 S t. where y is measured in meters and t in seconds. (a) Find the velocity of the object at time t. Simplify your answer to a reasonable degree. (b) Find all times (if any exist) when the object changes direction. If the object never Changes direction, determine whether it always moves upward or always moves downward along the axis. 5. (10 points) Find all values of .r in the interval [0.2%] where the tangent to the curve y : 3 cot .l‘ + 41: is horizontal. dzy £1172 ._ 6. (10 points) Find if y : sin (-31". [More on the hack] 7. (10 points) Find the equation of the tangent to the curve .1‘ : tantry) + $2 at the point (1,0). 8. (10 points) As water is being pumped into a pool. the amount of water in the pool . . . 300i . . . . at time t 18 given by DU) 2 f + 1 where U is measured in cubic feet and f in minutes. Find the rate at which the Eimount of water in the pool is changing at the moment when the pool contains 200 cubic feet ml" \x'aitei'. ‘) ll _ W2: 1. 75 0 Bonus: (5 points) Let fol?) : ‘1 0. .l‘ 2 0 Show that f is differentiable for all 1‘. and Find f’(0). Determine whether 01‘ not f’ is continuous at 17 : 0. * .L - ,3)“ _ ' ‘ l.(4)£":’;z ( X’Z. x5? , 5:: X3“! = L»; ,1 ~ _‘ y—qz {+2 “ I? (WM_H%I(|—iL {M MAO-LL Jk-ao ‘9‘ Ja—ao' 13M —- i _ ' —’2t1+’ Xk—ao. a + ’9‘ _ £132“ 7 ‘= " °0 {z 7<rZ~zv A ~7C+?— t L”. ,f... Y-‘PZ. (mu/x4) 9+Wc> M M) _—_ (:‘70 3t(3+fq':t 2(W‘3 M ¥(x\;m m :IC+3 x-wl” )0?!" So M W \)C+3 3L’ as 3/4 9: I3 3 It”) :- M 16%) 4/0) i If}: ’1 Wu jA-lw A A4") A T &+) : 31W {-(mnB M -w- {N90 «(AMEN t JA—ao $71710 : M _,L _. 0 4x40 4,711 k 1+ 1’“ 3&3 = t7 0 k/tzwr ) / \( 1.1. —’/2' \l ‘3: SwXJr‘Wf g, 3 ~3wcL¥ +4 ,O':o 3-1—560ch w to Z __ 9/3 = 3m7'm‘x) . cushy). 5‘ : (S'ym‘fo) cum) _ /g(&w(§X)‘w;-(5K>5+ Wz{gx)(~§/ML(SX)'5) up 9: 9 ~ 125 (Zyv‘vJSfl c.0950 ~3~L~51§xfl '- : #SC ng>( 35“,ng ~8~1~Z€x§ 77. sz—WW3>+7CZ 51;”); % (MRS) +36) If» xw, W WM): Y; z. = (l-mfl «33%) -<I~:/f¥> fl Y3O) 4/2“ fire} z/LM, Llh)~~£lo) ,{Aqo A Y)»; (l—aah) _ 0 $90 .44 “A 1 )2»; WWW“ jA—ao in“ A - k 7—— t 32:; U i: 3 « 0 1+.SMM PM ‘3 W {Ad/(pg), «awr‘m'm Tszmgo, Wm, 4—» 2 v (l T § 7< \./ a ‘1) 74K \J (\x )T ")E \< v {v ...
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