Summer Final 2015 Version 3.pdf

Summer Final 2015 Version 3.pdf - University 0f Ottawa Dept...

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Unformatted text preview: University 0f Ottawa Dept. of Mathematics and Statistics Caieuius III for Engieeere MAT 2322 3X - Sprieg-«Semmer 2815 Midterm I ~ V13 Prefesaer: Abdelkrim E1 basraeei Daration: 89 minutes. gaggle: ID "xaznher: Instructiens; {Please mad {firefight} «- This exam has 8 pages and yen have 83 minutes to cempieie it, o This is a eiesed beak exam. c The enly calculators which are aiiowed are those apprm’ed by the faculty of science such as Texas Instruments T1303 T1434} Casie iii—268 and fat—3002 scientific and non programmabie. 1! Read each questien carefufly before afiswering. o Questiene 1 t0 3 are multipie {‘hOiCQ questions. These questions are wart}; 2 paints each and no partial marks are possible. Please record your answers in the cor- responding bexes in the grid below. 0 Questiens 4 to 6 are ieng amswer questiens. Questieas ii and 6 are worth {3 marks each: anti questien 5 is worth 37 marks? so organize year time accerdingly. A correct answer requires a full, clearly-written and detailed solution. 0 Answer each questien in the space previded? using backs of pages or the extra pages at the end if necessary. o D0 not unstaple the test. 0 Coed luck! E Questiea Q1? Q$FQ3 Q2? GTE Q6 E Tetaié _ M aximam § WWW — -# 4.“..— M#~‘1‘—'—- mafi,__z a ' V § § Answer , { i w W - awwém—a z E Seep; E [ . i i __,E 313313” .2322 3X » 23325263323 I :2 1, if f 2‘ 3 3;} : 533?? ~%— 325;; —~ 53:33: Whig}: s32? fizz: 2333333333155: exprééggmzag mrrz’zgpiznég :53 £333: 1:33:ng 1:333:33 “$0 1:333 gragéi {3f 5' 3:5 the paint i 1, E: :2}? A, z: : 211$ - E} - ’52:? ~1}- :2 B. z a“ 133" w ’33; w :2 C. , 3: «3 E1 /w k” ) gm. 1‘3 W “mm vi 3:: I 1...; W' W?" i M CD “+23 2 M mm» 3%“ W F. This functieg is 11:31 differentiabia at the indicaégefl paint? $0 the tangent plane does: m3: exist. ' {7’3" 33 34 :92} 3.5 93‘: , 2/ w : 3 / é -’ ,, 3 2 x? W :3 “g: M 5 Ex 3.2;} i 2. if fix 3;} 2 63;”2223‘2. anti 2? is the unifi meta: along 2;}: which of the faliowing corregponds to the direfitional derivative Dgf<2, 1}? A: 86m 2 gag“ WW MAT 23252 326 A 333353321333 I 3 3. If fig: 3;} :2: 3333 3313:} E? is; 333133 38332133333333 333333833 {iefizzéé 3.2:}! {I g :2: <1 E? {:3 :1: 3; g 2 3331213 3:3 iize 33311133 Cf £3333 (162131133: 333333333 // f 3534'? 3 is: i s A 3 2:3 :3 ‘3 3 \ “3; 33:13 W 3‘ i 33 333 {i}; B 133 33:33; i3 3 3“ 3 Q ”a: ‘ . 3’ ‘ 3i 3 3 g 3 ‘3; ‘J C 233 :3. 3 W 3:. 333 1?. 533 a a, 222 .V 2 W22, aha? {6221:2822}. 2232232213 2:22” this: {Sasha/222 j” 5 2 '3; 2 u E 6 V . ,2 Ma: 3 2%: i 2?. :3 M i: MAT £23222 3X - 4., Fimi 2222222 833 03 Mg? 23:12:? 3K ~ Mfiiiéflfi 5 53 F2316. the 23%}:38313333 {gamma 3:33;? migfzéfim {2% {.3133 {BEEQEEGE’E fix g} z .3: ~f~ '53 {31: £213: :"egiazz ‘c ‘< a ‘9 33% 3$§W§33 ‘3” <3“) MEET 2322 3X ~ Miéiemz 2' 6. L5: 2‘? 1553 {$25 Emmzi‘ieé 55255:sz Effié‘iijfifid 53535555525: the 555255625: ;: :r :53 é» :2 55153 55555555353355 Q 5 _ ,3 _ : 3;; : W213? 21-1253: ihe iimg :5 : «2 251355 :5 r: I in {i153 «5735;315:253. 8:551:55: aha réégiea R 55:53:; campuie the {giazzbEé imegmi // 5:3; 521% 5 R {5‘ fl 4 5 EL’Q’E ““ f a 1,», ‘ , a; 3/: ‘2‘ , i: : 53;; :35; :5: EM E ‘5 a ...
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