Ex1Sol - Math 21C (Spring 2005) Kouba Exam 1 Please SIGN...

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Unformatted text preview: Math 21C (Spring 2005) Kouba Exam 1 Please SIGN your name here : _________________________________________________________ __ Your Exam ID Number ________ “H 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. [T [S 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 WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. No notes, books, or classmates may be used as resources for this exam. 5. 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. 6. You have until 9:50 am. sharp to finish the exam. 7. Make sure that you have 5 pages including the cover page. 1.) (10 pts.) Determine the distance from the point (0, 2, —4) t0 the center of the sphere given by 1:2 ~ 41: + y2 + 6y + 22 : 100. (K’LLM +40+Lyhey+fl + 233”: (oo+<{+C1—~v @4424— Ly+3jx+ @wfi: H3 —a W '. 2/‘3/0) M L: LZ—oj’M. G3_72/2+,Co-~</)1 : 1%!5 2.) (10 pts.) Find an equation of the surface in three-dimensional space formed by revolving the graph of the equation y : Ina: about the :c-axis. 4.) Evaluate each of the following limits or determine that the limit does not exis ,2_ 4 “3" . x X (1(lpts.) lim 1: y g M Cxaj ) t7 ) ($,y)—)(~l,1) .“L' + y2 (x/y)—> (-ll 1) X F/ 1 ‘— G/l‘fllj‘z: “l b.) (10 pts.) (fig/$0.0) $4224 : BO— D/UE W '. Eefl x:o ; ~92; : M O 3 0 {j \l/ Qxly/—>(9/o) 3’ (xiv—9 (o, o] x“ W M- M X" r M ~ : J— m; ' (X/YJ——‘7~Co}o) X“+X" LX vj—rgoo/ 53% 9V 5.) (10 pts.) Determine the domain and range for the following function and sketch (shade) the domain in the airplane : f(a:,y) = V25 ~ 11:2 — y2 . 15‘ X'ZWY‘Z 20 -—> Xgl—flf 5/ .><*+y%:...s.?). :6 ,L if: ’ig§;x2{z‘¥;§>.:>><?i7f¥ €525. % - -. a —j’s‘><ss’ ‘ i 1/25.“ : “abuser boma / Range: 0 i .8: f b 6.) (12 pts.) Show that u(a:, t) : C_tSln.’L' satisfies the equation uM : u“ —~é: .% —~(: UK: 6 mx M : 3 '—‘m)< I "C MK M w “63 M ~ JC X j 7% LAXX are 7.) (16 pts.) Find and classify (relativemaximum, relative minimum, or saddle point) the critical points for z : 2:114 — $2 + 33/2. ZK: 3X3v ax :_ axfilxg—l):o “am J Zy:(oj:O——>|j:ol )- fiw W ((50% (“ii/0L Owl/0Q Ciao) 5 __ r1 __ _. éxx— 24X~£2J£77céj %X -o 7' 5 W) '- D: ‘3?“ iLW‘i '37:; : (-2](é)— (0)92: “1:,2<o M w W a E: O) ' J w); 9: Zxxilyr £3: GUM-cw; m >0 8.) (10 pts.) Assume that z : f(:1:,y), m : rt, and y : 2t " r2. Compute the second 822 partial derivative SlMPLllfi‘Y your final answer. D g: : ZX'§%+ arr-Di; : zX-(+)+£y-C~2w) ———> a?» z.) 32 “a u . Bf; = 5;; SF) “ fiE‘EX a”) 2%)! (2%)] ~ 3 3/ . " {ix fictlil" aw (EEK) be) if 3 3 ~ Eff ggQJZv‘) 4- 57,7633] 'CD'W‘)? _. B ‘ zx'c’) + [gxxgg'ir awe—37] (f) B '3)’ " 3ft?) [Zyx‘ 5%+%w fill“) ll [EKK'G—N' ny'c‘zvjlcf) ’“ 02E)“ “ [zxy'C‘H 1" Zyy'C—RV‘2} Car) : ZKX'Céaj— izxy‘CqY‘fJ‘l‘ (,L/V‘z') "' The following EXTRA CREDIT PROBLEM is worth 12 points. This problem is OP— TIONAL‘ 1.) Determine the value of fy(0,()) for the following function : . + 3 . Hazy) = { 51:21:: ) M14331) # (0,0) _ ‘ >< >’+ln ~— L y 4‘7 Q972~ If??? lhfl—M {A ‘l’ X) ) —~> 41>, Lo 0); M ‘llf0,0+l\2‘-‘l'§6!0) ) Vl—V’o ln 2 ‘Lcogl‘J-“O V190 h - M flu. ’ l/V’o la2L l4 3 {AW “we? : 1 +0 ...
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This note was uploaded on 02/17/2012 for the course MATH 21C taught by Professor Milton during the Summer '08 term at UC Davis.

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Ex1Sol - Math 21C (Spring 2005) Kouba Exam 1 Please SIGN...

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