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math244 winter05 quiz1

math244 winter05 quiz1 - Quiz 1 Math 244 W1 05 Name ‘ 7...

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Unformatted text preview: Quiz 1 Math 244 W1 05 Name ‘ , 7 ,, Show work for full credit. No calculators are to be used on this quiz. l.) (lO)Solve the following separable D.E‘..: _ Xx A») 5 (W) 77’ /’;' fl: \ (lo/‘9 > 1 / V (9’92) ‘7 ML) «film 13-5] ': ya» C. URL 940th ’p/ALA'I‘Dflfi: Q; Q 4Q * ("”533 i” 6* I , A g 3 9 ‘1 . y C ”Mk/‘93 44%;“ AA SaMJc-laims may.) AU”) “:89 beznwfiz 9 9‘5 alarm“!- «4:, I ‘ 53"f3 Z ‘X'ESA'93JZA/’: “ : 3 x A A94 3"; ’ lt): CG ;.J\7 ah\‘fia\ ; Q3 A‘9(A-5>_—1 ;‘\ A’B : a A z 3 5:\ 2.) (10)Show that the following first order D.E. is homogeneous, and solve it. (xy+y2+x2)dx - xzdy = 0 I Z [gnaw (501+ 04—316“ _ (m :15 so Z Z :1 gm” +144 +2213,” - 15x 1: o ?)¢Ur ; “(~1x7ah3‘ / 3.)(10)Match up the following D.E.’s with their slope (direction) fields. Show your reasoning for each. Each D.E. has only one \v/ slope field. D) ( yrzl 310?; 1:5 «(Mag 1 ’wmuvhou‘f‘ 510% gig /flk 50 C I '6 (OV/(t—I' «HSWL I‘J 5’09: 35 A Mugs gas/4m». 52> B, D) AHA f (OHM War/t eyu€+ +1.1, 57962, '35 0 Law [f .1: 0 $0 4%»‘7L Ma, Le, 5 Km +1“ “"97““ «WSW ~~~~‘\\\\“:7‘IIII Irrao .1 lllllvp-2__.—vlllllll II’I’III’I’ZI""IIII' ~~‘~“\\\“|IIII I'll} l!!!/:aa-- -gaaflllllll "”””"’ ”””III1 I ~~~~\‘\““'IIII 11"; I IIIII‘a—u -—-'aIIIIII I Illllllll ’;¢;,,;,;, I I I “~‘\\“\‘||IIII lilac IIIIIIr—g- _--‘4’IIIII ’l.’ ””’ ””””” __ __ Illllflllll IIIIIIIII ~~~“\‘\‘\|IIIII III/4 I Illllaa -.;IIIIII , , II III II ““““““IIII Ilddl I Illllro-- --.—4IIIIII I I I IIIIIIIIII I’IIIIIIIII III! x‘.“‘\““IIIII tray; I IIIIIa— - .arl’l’l' III’JI IIIIIII I I I I ““~“‘\“lllll (roar IIIIIII— - —alttllll ’ ” l ’ ” ’l’ _ alrrilrtarl I’llllll o ~\\~~\\\\\||'l” "I I I'llllo oarIIlIIl , Iltllflllll II III ~“““\“‘IIIII III I III/Ia. .. a—IIII’II ’ ”" ~ I'll Ia! lllllld— . -pt'llll' ’II””I'I' Illifll’l'l IIIIIIIII IIIIIIIIII _2\\\\\\\\!I"'l ”’ ._ "”"‘ "”””2 ’2’ ~\“‘\“-\‘.IIIII 1”; I Illllrp -—4’IIII IIIIIIIIII Illfllllll ~‘~\\\~\\\Il"" t’;r4 ,{/,,,,, ‘,,,,(,ll IIIIIIIIIII IIII’III/I ~\‘~‘\\\“‘|',,, ,”” I (,,,,,, -nd’llll’ IIIIIIIIIII I’ll/I’ll] ‘~~“\“\“‘Illl ,”" I ’,;,,,— .,,,;[(ll IIIIIIIIIII Illlilllll ‘~“““\“‘IIII (It‘d I Illlld— ‘41IIIIII IIIIIIIIII’ IIIIIIIIII “““\“4‘\‘ll,’ 4"... I Illlraa— -‘d’l’l'l Iallltllrlt IIIIIIIIII “.“\\\\“‘Illl Irora I Illlta'- a-coIIIIIII I’IIIIIIIII IIIIIIIII! ~._““\‘\“IIIII I’Ilr I IIIIIa—- ---—;IIIII-I It’lllfllll IIIIIIIFII \\‘~\“\“‘lllll Ir’aa I Illlraa— --——’IIIIII IIII’IIIII’ IIIIIIIIII ~~‘\~‘\“‘_2|111 ,,,,, I IIII’a—._2 ---—Irlllll (It’ll/'rt—ZIIIIIIIIII v E v v - . . IIIIIIIIII/ZIIIIIIIIIII II ,,2,,, ‘ “‘\“‘\“‘7II'IIIIIII fi IIIIIIIIIII IIIIIIIIIII ,, ,,,,,, , ‘\‘\“““‘|IIIIIIIIII Ill/IIIIIII IIIIIIIIIII ,, ,,,,,, , ““‘\\““"IIIIIIIII IIIIIIIIIII IIIIIIIIIII ,, ,,,,,, , ““\““‘|'lllllllllr IIIIIIIIIII I’ll/Ill!!! ,, ,., I’, , ~~ Ill//;,,,, ’ \~\\\\\\|I I ll’latrrr Illlllfrlll ,, ,, ,,, I “““‘\\“'Illlllrtto III!!! II I II ' tr r rrtr r Ara ,, ” ’I, I ~.“‘..\‘\“|Illllva;’a rtdaa—trrda —””I¢a¢pr II ta -aa I ~~~\~\\\\\\ll’flradra— a—r.--.aa—. —,.oa..—... ,, v— --. 4 -~~~.~‘. Ilrtau—.-- —--—’——uc—— ---’———‘-—— ‘\\| _- l' .- --— I -------...“Ira---—-_- ‘ ' - II - I ----_ --- ’ .. 1 --..------ ----------7 ~ ----o..--- -t----.-..:t 7 ‘ z —?""' "’ \ ~\..\.~..~ ..._..~.~~~ , ‘ """""’ \~~~~~--~- , ——'—aaollll \\~~~\\‘~s\ ~~s~~~~ss~~ , “““““ , a-.—;a¢’rll ~\\\‘~\‘\\\ \\\\\\\\\\\ I '\\“““‘ ~ I artatllllll ~\\\\\\\\\ \\\~\\\\\\\ I , "““““ raaattlll \\\\\\\\\\\ \\\\\\\\\\\ I / ,' "““““ rrrflllll \\\\\\\\\\\ \\\\\\\\\\\ I , ll, "““““ 4411,11! \\\\\\\\\\\ \\\\\\\\\\\ I , II, l“\““\‘ IIIIII’ \\\\\\\\\\\q\\\\\\\\\\\ I I ,II' "““\‘\‘ I’ll/ll \\\\\\\\\\~_\\\\\\\\\\\ I ’II' "““-““ , IIIIIIIIII__7 -Il\|\\\\\s TABLE OF‘I-NTEG‘RALS} BASIC: roams du ‘ ,1. Ind!) - uv -— I win 6. J‘s‘mudu = -cosu + C 11. J‘cscucotudu = -cscu + C 16. J.—--—-s‘m" + C Jazz—u1 a l 4,. ‘ 2- II = II + ' - d ‘ fudu n+1" C 7.J‘cosudu-sxnu+C IZ.I:anudu=-lnlsecul+c 17.! ., u l-ltan 'i+C a'+u a a n# -l d“ J. 1 J‘ - 18 f—-——da -'1-sec"-u-+C 3. T=ln|ul+C 8. sccudu-tanu+C 13. cotudu-Inlsmul+C - am a a z du l u+a 4.f¢“du=e”+C 9.!cscudua—cotu+c 14.J‘sccuduBInlsecu+tanu|+C 19- LII—alga“ u—a C I 1 I du 1 u—a 5. a du--—a +C 10. secutmudu=secu+C 15. cscudu-lnicscu-cotu|+C 20. 1 1 =—ln +C lna u -a‘ Zn u+a ...
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