exam2sol - Math 21A Kouba Exam'2 Please PRINT your name...

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Unformatted text preview: Math 21A Kouba Exam '2 Please PRINT your name here : __. ______________________________ ___________________________ __ Your HW/Exam ID Number __________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY. ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS \VILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. :1. Read directions to each problem carefully. Show all work for full credit. In most cases. a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages7 including the cover page. 6. You may NOT use L’Hopital’s Rule on this exam. 7’. You may NOT use the shortcut for finding limits to infinity. 8. Using only a calculator to determine limits will receive little credit. 9. You will be graded on proper use of limit and derivative notation. 10. Do not use formulas from physics. Derive all necessary formulas. ll. Put units on answers where units are appropriate. 12. You have until 9:50 am to finish the exam. l”) (6 pm each) Differentiate each of the following flmctions. DO NOT SIMPLIFY ANSWYICRS. D a.) y :: 1'3 - (:31? T J)‘1 -——"‘3 7‘: x1 wow/35+ 3x4. (ixqu ‘ ‘ 1,az1(3;z:) 3) b”) j m 5:851; “’9 l I xmx.m2(3>< Kyméx .[XMXXQMX+IMK] 41$) : CK MK D z D <1) 9(1‘) : [smcosSQL-fl) ———5 -I/ 9‘09 : TIL (M ngquw $60146“? 387/ @426” ' W657- 9x3 _ - _ /,‘ _ 2‘) (9 pm) use “In 530;” “33) to differentiate the function f(33) : 32:2 — 2:1: + 7 . #40 h \p'CX) - 40(44‘ ~4é<) ‘ o h 2:” SCAM/02s. {CXMWQ — (326— a)“ 7) 1 (A H , h abflmfiw—W ~AAx/~214+/7~/3x"+k26?/ _ M o : ‘4’§0 , 1’1 - M Xfiex¢3h~ol> H M’YO % : GX+ 0 v; 1 ®X~JL 3.) You are standing on the top edge of a building which is 256 ft. high. You drop a large. orange pumpkin and watch as it falls helplessly to the ground. a.) (6 pts.) Assume that the acceleration due to gravity is s”(t) : ~32 ft./sec.2 Derive instantaneous velocity, and height (above ground). stat). formulas for this pumpkin. 5“ _ 32 ,__,. y } s‘~’3,,2~6+9. ("6:0/ 3‘10“ 030+Q—aQ—To/a h.) pts.) In how m V seconds Will the pumpkin strike the Crro ind 7 6:0»? net—1+3 5: O —> _(©<:€;L__(@]:O—;9 c.) (3 pts.) What is the pumpkins velocity as it strikes the ground 7 5M : v 32 Cu) : Mme/M. 4.) (6 pts.) Assume that the second derivative of function f is f”(m) : x4(1; A 2)2(:1: — 4)5. Determine all x-values corresponding to inflection points for wO-—-O-—O+ H 5.) (14 pts.) Consider the function : 132(1: — 3) on the closed interval [- QJH Determine where f is increasing ( T ), decreasing ( J, )7 concave up ( U ), and concave down ( fl Identify all relative and absolute extrema, inflection points, and x- and y- intercepts. Sketch the graph. The first and second derivatives are f’(:1:) : 3x2 v 6.17 and - f”(;r) : 61: 6 r x231 X20 x;9\ Kw Y:,~OZO \{ZO Y1” W W W ~lLHCX): é><~ (o : GGH) : O X:",Z X:I qu . :31 ~l1~o ~Q<><<oj Q<K<q/ W $20 \l W o<><<.,z / (<><<<( 6.) a.) pts.) State the Mean Value Theorem (MVT). W [ox/b3 W 0-14 w W CleO), TMMW A4, WW W W C/ CK< (1(6) .PICQ): b.) (8 pts.) Determine if the following function satisfies the assumptions of the MVT. If so. find all values of c guaranteed by the conclusion of the MVT. y cosm, ingmgl ‘ZYZMX f($>:{:c3+1, if—1§J:<0. leil ‘ - M 471004 / Mic h z'f:“"*&l '- “70+ - k = 'f:2+ “1b’ =0 o (A war wig}: : first Ltawazéfifim l ->o a 4’0 \FCO):0 :9”on (:11) ) X21 Mvr 7.) (6 pts.) A beetle crawls along a thin rod on the x-axis from .17 : 0 in. to a: 2 10 in. at the rate of 3 in./min. The temperature of the rod at point :1: is 40 + 12\/E degrees Fahrenheit (0 F). At what rate is the temperature of the rod under the beetle changing when the beetle is at :1: : 9 in. 7 dx_3, // , _ _ x0») 3. M. M, 3 X—o 'chr kwo aT_ £32435. .L 72,19: our» ‘ Ax 4+ ‘ we“) we .4 o :(ocl'zL3jié'3l—"3 : (0 FM (6 pts.) Skecth the graph of f” using the graph of f. l I t l l 9‘) The following problems involve different types of asymptotes. (6 pts.) Use limits to determine equations for all vertical asymptotes for y=$2~l1 —-———~—-—--Q<6()Lx+l) ' CM X10 M X=\‘-> x:l:MW—2x— V..- xél KM‘I-(§LWM A] X.=_9.'- M W: —‘-/::l:00 w}V.A_ x:oi X—vo or b.) (6 pts.) Use limits to determine equations for all horizontal asymptotes for m 962”? ' x M K . X _ M I + ~ in .1, 25 x ‘oo £5 ’QQEDO V‘xfizfl 1X6“) “0+ xa) 4 M H x1 i w a?» ._. x—a+00 (+1548. H-o 'L M *1 A— =-1 ’6‘” ~2< Mg; ‘-m $ ~— c.) (5 pts.) Determine the slant (tilted) asymptotes for y : I $+3' X"3 x1 Cl — ~ X~3 4— “' X+3 ix; M Y' ><+3 ' 9%? ~Cx2+3><l “31:11 5A Y=><~3 The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is 011 TIONAL. 1.)UsetheMVTto provethat tancL‘2x for 0§$<7r/2. M X M WW wax o<x< 719—:— W ¢LX22MX mm W M Cng_ FM flagpmx: MK Conj _ Xvo 0 o l _ Mb—M ,1 mac: X”O lS—(fi- 4; : mx o<c__<"_7:)._§ M0_w{\c X 2‘ 76mm >l a “X H MXZX x934 0fX<E CW/ MOLD) ...
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exam2sol - Math 21A Kouba Exam'2 Please PRINT your name...

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