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midterm1-blue - 16B CALCULUS Francisco Santos Midter 1(even...

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Unformatted text preview: 16B CALCULUS Francisco Santos Oct 19, 2007 Midter 1, (even numbered seats) : ?WS'@ Sim/IV ID: 1. (6 points) Determine whether each statement is true (T) or false (F), then CIRCLE the appropriate response. Assume that x and y are positive. No need to show work. ® F (A) lnx lny = ln(a:y) T (B) fidx=1n|x|+C @ (C) 5W=5$5y T @2 2. (8 points) Find the function f (:L‘) which has the following properties: f”(:c) = 4-2 + 255*, f’(2) = 28, f(1) = 0. C . r V w ''''' / Mm: a/wze“ L; 5 "26 / Mflwfiw .......... .j Name: . ID: ' 2 3. (6 points) 60 students in this class know how to do indefinite integrals. Two weeks ago only 40 did. Assume an exponential law, and predict how many students will know it in six weeks from now. Simplify your answer as much as possible. Is it more or less than 150? C(p .: C(61); 6,“ 37C) ‘5” , file fla/Z\UZ« C (2) : <76) C¢K:KCR C(‘é/I— 1/ k2,) ""’ / ,._ v “,5“? 48$ 2 69K 66:/‘1C" %2 ~ (’IIC‘7 75 ': /g : , f A 4’ $631?“ It”; , ,» 7” ,7 Al 4 ./ '2\£/;2 _. ujig—i;32€’6 c(’z):4/6~65(铧6:9< / ~ [1 ,2 4. (8 points) A stone drops from a certain height, and it takes 3 seconds for it to hit the gorund. Assume the acceleration due to gravity is —32 feet /sec2. Let s(t) denote the height of the stone above the ground, as a function of time 25. Let Mt) denote the velocity of the stone, as a function of time t. a. Write (or derive) the equations for v(t) and 3(t). Um“ 321;” Us 2~32£ 550%? i» 5/5) s 5 (fl: _ mm. m 14 t 5(3): «ma/r, “09:0 b. From which height was the ball thrown? c. What is the velocity of the ball when it hits the ground? UCH: — go‘ fill/Ea Name: ID: 3 5. (10 points) Sketch the graph of the following function f(x) =1n(£2 + 4) — 2. Find all maxima and minima, inflection points, and axes intercepts. The graph has no vertical or horizontal asymptotes. Say why. ° E0.) [Mugs mg Slate £74): 1: 40 M [$41) :g—E2C3/ 2<+‘1’ / MWVMI 9 A; WVéic/oi avapilorlty‘ 52W VLJLK OLA/“WU” L5 “fl ’7? Cn’ W C; ¢W;MWQ"LtL 5:: Jlu‘ €14 l> " ” m ”ME: “““ WM gH/M 5A (24ft : +aé/ (:[W {'14 C899) .:+o¢ X'790 A") ””36 Name: ID: 4 6. (12 points) Evaluate the following four indefinite integrals. Simplify your answers as much as possible. Show your work. etc. v ~~~~~~~~~~~~~~~~~~ 7 ~x’ ,4 / a. f_2____e:+1da:= j/(CK *Q ‘jdfic _:/€" .- 6 + (4 if / , , I — 3km beam/we, .4 gkze’“ Col/d 3’8 X: -6, J 5% K (12¢ a «' l 6 + 1’ b. I 6z+1 611': bOCEX/ VVLQGKIM'IV /"——fi— 2L LDCJX ,. / 2X 37““K “'1"? ”I " .. ‘AGM i5 CM CkZ/lgC/I arr/2‘ $0 MT € 4; 5AA) lpcajllér/ Gui/MM} . M ”" ‘ I ., ‘ [AP/Y [90‘ Y [7 (J! 6 7‘0)? [ii/“1 ,. é) If (”affix \X‘LI L1,? J LVLQ’Q/M d f6?“ 5dx= 3—; \ P>A'5 / {/Z/Qvg/ ,‘L gfik’ f 3 C Wt jflmd dirk /’/3*“5 t / {'3va { C Cflx = ; L: 6— <1 5 .57 W—‘J ...
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