exam1sol - Math 16C (Fall 2005) Kouba Exam 1 KEY Please...

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Unformatted text preview: Math 16C (Fall 2005) Kouba Exam 1 KEY Please PRINT your name here : _________________________________________________________ __ 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. 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. 2. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 3. 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. 4. You will be graded on proper use of derivative and integral notation. 5. Put units on answers where units are appropriate. 6. You have until 8:50 am. sharp to finish the exam. 1.) (9 pts. each) Use any method to solve the following differential equations. You need not solve explicitly for y. a.) y’ : 4x3 + cos 4:1: — sec2 :10 a b.) y" : 462$ + 122: — 6 2X 2 71:44.;Iic +(ox v (ox 141/ XX 3 ._L ‘1 MM xe’< A W33 = ex a €x71+axj : Q1?) x ~ CMX'L A DLQJ)- K ax): 2‘) (12 pts.) The rate at which the amount of money ($) A in a savings account changes at time t (years) is proportional to the amount A. Initially, there is $1000 in the account. After 5 years there is $1500. How long will it take the account to grow to $5000 ? K‘E’ Eli: ~——? ,4: CC v f:oA:1’f/000~—v " / M 0 k6 (oootce :c-lzc «a Azlwée f35j43f/é/OO —-> /5’00 Imooefkfly , ’ 5 :6,qu fizz/11.52146, k“? Mk5: 5k —=r K: 1.5—? _I, A z [000 A: fé’ooo a J. , , Lit/“4152f 5000:1000 Qtyflmlgjéi-a b :C ’7 My: c, e (Lb—MWMJ M{:&Mlo5)‘é —a 3.) (8 pts.) Show that the equation $2 +563} 2 C solves the differential equation 1323/" — 2(x + y) = 0. xl+xy2 C 2» a><+xy’+t-y: o a» UL x+x\/”+ Y'+Y’:o ——, 4.) (8 pts.) Determine an equation for the sphere which has a diameter with endpoints (—1,0, 1) and (3,2,0). 5.) Consider the equation z : 9 — 1:2 — y2 . a.) (3 pts.) Determine the m-, y—, and z-intercepts for this surface. X20} \lzo —» £2 “1 xco/ szoq y‘zccl“? y3i3 ‘2 ‘ _:l: 3’ y:0/g~20—» ><:"l—> X~ b.) (3 pts.) Determine and sketch the 3331-, a:z—, and yz-traces for this surface. 3’ c.) (3 pts.) Determine and sketch the level curves for this surface using the following values for z : 8, 5, —7. E28: 3:7—Xi7'z—a X3+7:/ 5:5: 527~><i>ltxif=fi iz~7z~7=evxifl-xh§7i d.) (3 pts.) Sketch this surface in 3D-Space. 6.) Water containing 2 pounds of salt per gallon flows into a tank at the rate of 4 gal. / min. and the well-stirred mixture flows out of the tank at the rate of 3 gal. /min. The tank initially holds 50 gallons of water containing 10 lbs. of salt. Let 5 represent the number of pounds of salt in the tank at time t. a.) (5 pts.) Set up a differential equation which describes the rate at which the amount of salt changes at time t. éédmmmmw) “ =c°f£l<igj~ (gyms—g) -> olS _ .3, .8 M ‘ 8 501% b.) (10 pts.) Solve the differential equation in part a.). Determine all unknown constants and solve explicitly for S. 3 550+EM 3%Cfoi-‘6/ A S + 3 , S 2 8 ——’P /l‘/\ : C : C M 504-19 3 -; (5-04—1923 ——> C50+f)3.:~§ + 3(5o4—e)". 5 : 8 (5‘0++]3 “a D ((50+{v} 3. 5) ; 3(504—fj 3__, C50+£J35 3 5 3031-9291“: 2(b'o+f)‘<+g_y ‘0 :— 9\ £50) + \Q—i _——» : ~?o(50)——->2 (593 3 - S: l00+6H~——?o(50}‘(5o+£j 3 Each of the following EXTRA CREDIT PROBLEMS is worth 10 points. These problems are OPTIONAL. ' 1.) Solve the differential equation y" : y' . MJCX)Cj/‘ 77/441 YHSYI'fi 3(Cx):jCX/——7 jCX): CLICK WV? j:(’,€.———=7 ...
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exam1sol - Math 16C (Fall 2005) Kouba Exam 1 KEY Please...

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