exam1Bsol - Math 17B (Winter 2012) Kouba Exam 1 KEY Your...

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Unformatted text preview: Math 17B (Winter 2012) Kouba Exam 1 KEY Your Name : _________________________________________________________ __ Your 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. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENTS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. :5. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read (.lirections to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. N eatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page. (5. You will be graded on proper use of integral and derivative notation. 7. You will he graded on proper use of limit notation. 8. You have until 10:50 a.111. to finish the exam. Students who fail to stop working when time is called may have points deducted from their exam scores. Thank you for your cooperation. 1.) (7 pts. each) Use any method to integrate each of the following. DO NOT SIMPLIFY fl‘IISWEI'S . a.) /x(x3+2) dz l : 3(x"+2x)oL¢< : 75K #M b.) /(.‘L'+1)(;1:—1)8 (LE UZX~I 2? abut: M M X: M‘Hj : SKuw)+/)M30(M : SCH+9~JM90LW : g<uq+azu8) J“& c? ‘1 : Lu“; 2m Jr e -; —‘-<><~/2“’+io<~l) w (6 a] ‘0 Cf 5:1, X’l4—C, c.) /sec10m-tanm d1: : §qu.mx7tomx9‘kq ‘ m :SqaL‘~;» ( I . lo 39* :MX —_..AM (awuzmxmxo‘x ’0 q+Q'lb(' qurc z+1 x4»! A B M ‘1') 1 WM =MY+5<17 : BEIZUV—JL-Iv M \“\:("'z°"2) :. legq+gfl41u+ll +C, ~ :- x— 1476+ z/«vxlfleJrC: l 00 p :3 c. (Q < (B 5 6 2.) (7 pts.) Assume that y = f(;1:) is an even function with [0 f(:v)d;c _ u 00—2 “33) (11‘ = 3 . Deter'rnige the value of /:~f-($) ch' . ~ % flfi 3. WW rt +62% ~ 3’ M a 4, siwwr-ikam: Wmsll :44 WW} 3.) (7 pts.) The base of a three-dimensional solid lies in the region bounded by the graphs of y = y = O, and :L' = 4. Cross-sections of the solid at a: perpendicular to the .1:-axis are semi-circles. SET UP BUT DO NOT EVALUATE the definite integral which represents the VOLUME of the solid. 4.) (7 pts.) SET UP BUT DO NOT EVALUATE the definite integral(s) which represents the AREA of the region bounded by the graphs of x = y2 and x = 33/ + 4. x: 3Y4. q Y2: mm a 71-— sv~q:o a CY~H)CY+I):O —-9 \(:~//\/;qj : Sq —L€#)clf = Siteww 4y 5.) (8 pts.) Use the limit definition of the Choose equal subdivisions and right-hand end 03% [a]; it way definite integral (for convenience, you may 2 points) to evaluate / 3:52 dry . V10 MOMMA/‘4 &~ A . 0’; AXZ Z V‘ : l) o W (VIA F— ’1 —+—-—r-—--1--—T—-r——————’r‘—+ Xo x) X; X3 Xé:_;‘7:(" _ .4190: 3x’% J / A W S 3X1M : M Z‘i'CXL] AXL ° Have 5-1 _ ' 7" .22, : m L] ,4 - M .3 36?)"- 3.:— - new.czl .. M 3 3.3.3 § 14-500 "Ft “3 : M 31 L’” Vi-soo “’5 1:1 : Mieilm n+1 (0214+!) M-fioo'h3 X L ) _ M q._z{’,<w+l}.(/&Vl+l) ‘ W '4 '4 14—300 0 0 .. l+‘)' e1 : : \ W300 ( fi 40%;») 6’ 6.) (7 pts.) The depth L of water in a tank at time t hours is L(t) = 7 + t2 feet . Find the average depth of water in the tank from t = 0 to t = 3 hours. Avg : —‘—-—- )3C7-F‘E22M' 3~o 0 3 : é'(7‘é’4"3('+3)lo : igtal+72~~§to+ofl : l0 7.) (8 pts.) Find the length of the graph of y = (2/3).“133/2 on the interval [0. 3]. l_ .‘L I/ ' ‘/ ~ 7%" = V" W o = 53m A« : jg—(l-LXfZL/j :- %t4)36l firOf/L :ew e : 11 5 8.) (7 pts.) Let F(m)=:I:-/13E2 t2+3dt. Find F’(1). 2—9 X1 :‘oq: x- DGTW aw)+ 0) 3.1/9” «4+ X2 : x-W.2\x+ 83/954» M l 0 HQ): JET-1+5! +30% (M LA:€,X/ dv:mx c}? q (424:6,XM J v:Mx/ . X. ._ ‘ : ex/wnx- SCAM/IX Ax [MMZCX/ AV~MXJ7V " .2 abate/XM/ v=~caaxj =CXMX— ["excodx——" Sfixmxo‘x] :CXMX4—QKWX v 3exmxolyv v»; ‘1 BCXWX 0% 1‘— CXMX+€XC¢<IX+C .27 7‘ I . SC WX 0% : ZCXMx+-_iicxwx+c: 10.) (7 pts.) Consider the region R bounded by the graphs of y = $3, a: : O, and y = 8. SET UP BUT DO NOT EVALUATE the definite integral representing the VOLUME of the solid formed by revolving R about the vertical line :2: = —1. 5M adv y M M ACY): WIR'L~ TFY‘L (A :TT'<\{/3_[/'ETFG);L/. z Wkifiwér'fitfi n-afih, The, following EXTRA CREDIT problem is OPTIONAL. It is worth 10 points. _ ,.2 1.) Use any method to integrate : / 1 (1.7: . ex, 1 Z X _ 3 l—— Jxx Q M ‘ ><-L x9. 6 C ’1. e*-2Xl€x (l w ((9 X {n p >3 @331 X g X :‘ 3 i9 (Egi ‘ 63144; ...
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This note was uploaded on 02/17/2012 for the course MATH 17B taught by Professor Kouba during the Winter '07 term at UC Davis.

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exam1Bsol - Math 17B (Winter 2012) Kouba Exam 1 KEY Your...

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