exam2sol Kouba 17B

exam2sol Kouba 17B - Math 17B Kouba Exam 2 KEY Your Name :

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Unformatted text preview: Math 17B Kouba Exam 2 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 STUDENT’S 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. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions 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. Neatness and organization are also important. 5. Make sure that you have 8 pages, including the cover page. 6. You will be graded on proper use of integral and derivative notation. 7. You will be graded on proper use of limit notation. 8. You have until 10:50 am. to finish the exam. 1.2 1.5 1.1 0.6 0.9 0 0 0 0 0.8 0 O O 0 0.7 0 1.) (3 pts. each) Consider the Leslie matrix L = a.) How many age classes are in this population ? q b.) What percentage of 2—year old females survive to the end of the following breeding season ? 70 ‘70 c.) What percenatge of 3-year old females survive to the end of the following breeding season ? O ‘376 d.) What is an average number of female offspring for a 0-year old female ? l o a e.) What is an average number of female offspring for a 1-year old female ? l v 5/ 10 20 . f.) If N(0) = 40 , determine N(1) . 30 f L; L5“ 1.( 0.9 ‘0 xaL3o+q4+IP loq .. &0 Ct at ( v o 1 : N C l 0.1 08 o q o W W o o. o 0 ,2 5» a O 0 0 ' ,7 o 3 o X . . $+y—z=4 2.) (8 pts.) Use matrix reductlon to solve the system { 2x + z 2 3 it~l4 ll‘lqKN1‘:i A) f a o l 3 O ’ l 3 "é o i {2 3« x Y 5— 3 l 0 4L /1 _L ~ 2 Q C) ‘ (5L /1. Y ~' ‘3 % x 5/ Ti. ' /sL 4-8 d 3.) (8 pts.) Solve the following differential equation : E 11262” ——-" dar: g—L 0W :SCQX‘Q")? —‘3 \{a —-_L _ 1 2X4 .Y ' (1/ 4.) (10 pts.) Determine the equilibria for the given autonomous DE. and determine their stability using either the sign chart method or the derivative method: id];— = 3N —N2 :: j M . / ,_, N, v V v v i, - , n. o + o - ' t - v M jaw/0% jag/-3 pawn N:O [0:3 / 5‘60): 3>o M N30 W) 1‘ Mfiim v// 3163/:3_é:-3<o Aowz3M. / 1 0 5.) (8 pts.) Determine the angle 0 between the vectors < 0 ) and (3) . i —2 W V - W) i —— y 7.) (14 pts.) Find eigenvalues and the corresponding eigenvectors for the matrix : Map/Ma’u—z ~<v{ : AKVA~é : CA~3/(A+2):o _—-, Az3/ ,\:-—az (A—A1)X:©t Alz3 (if; ‘OQFK—s Xl—2X&:o MM K13‘é iii—A X,=&~é4_a km: [1* :+[,"3 44, M WHY) 8.) (8 pts.) Determine P2 (36), the second-degree Taylor Polynomial centered at ct = 0, for f(x)=\/m. “1/ 4:0“) ) ~F(O() 3 2%: LX442 A M am I ’——-—-'" A—U’ -l ( l {L ammo)- «nil 434:9); all 1 i 0' o( 'T“/ L; ll l ‘1/ “Q -( “/ “a‘VFC): 3112 A. 1Z— M a: v 3 9.) (8 pts.) (Mixture Problem) Let S be the amount (pounds) of sugar in a tank at time t (minutes). A solution containing 2 pounds of sugar per gallon begins flowing into the tank at the rate of 5 gallons per minute and the well-stirred mixture flows out of the tank at the rate of 3 gallons per minute. Initially, the tank holds 100 gallons with 20 pounds of d sugar. SET UP BUT DO NOT SOLVE a differential equation for the rate d—f . fir Jinx moM/at Mn 42 <4 2 (I (\ 79 E v E l (A m E 10.) (8 pts.) The following data are plotted on a semi—10g graph on the following page. dN Use the graph to solve for N and determine the growth rate R in autonomous form. t N 0 7 1.5 19.8 W 3 56 Z 4 112 l _ f + g, 0 x» 5.5 316.8 [OJ N W1 3 C 7 896 0.4"er —-» l035é23m+1037 ——», 3m:[o<75'é~/077__, 3lm:10\7(%)~3 Wt: milojii/j—«r “At-1‘55;— H [OjA/t‘fi'l032+l057b a“ {V lay/V ‘6.l03o'L—l/]oj7 [03% {0‘77 0 o ’ lo “5 IIII II I" II II III. nllu nulnlllnllumfiflflfiflflh': Illllllll IIIIII I I All IIIIII Ell 0 l 2 3 4 5 6 7 8 9 IO The following EXTRA CREDIT problem is OPTIONAL. It is worth 10 points. 1.) The points (0, 0, 0), (1, 2, —1), and (3, —1, 1) form a triangle in three-dimensional space. Prove that this triangle is a. right triangle. ...
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This note was uploaded on 08/15/2008 for the course MATH 17B taught by Professor Kouba during the Fall '07 term at UC Davis.

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exam2sol Kouba 17B - Math 17B Kouba Exam 2 KEY Your Name :

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