# quiz_08 - .0 F08/0L9/01 0 16s MATH 2451 quiz_08 T,c Use...

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Unformatted text preview: .0 F08/0L9/01 0 16s MATH 2451 quiz_08 T,c. Use Exam ble Calculus 1varia Mult' Course 25 min 0 0 Duration 2016*03-09 (Wed) McCary o 0 Due Date Instructor Net ID 1!..III!I.II.. . I! iiiui: Z: \1-1 m N t "5 r .1 F lr\. ghi CV m. a Mr /L A M O @ ® [email protected]@eeeoeeemﬁ[email protected]®®@®®®®@®@®®@®®®®®mM [email protected]@@ [email protected]@aaaamaa [email protected]@[email protected]@@@em6 @®®@®@®® .VH,[email protected]®@®@®©@ @® 5 [email protected] a®®©@méémﬁ @®@ I aeeegaemxea maxeeaénee @eeﬂeevmzeavmzw @@©®®®® w e e e e @ @ e e @e @E @ a a e mwmegmw a u ,‘mme @e @e e e @@ @ gee @e @ e @e a e ® ® @® ® @®@ @ee e @a W1 @Emaev ® 0 (Last Name) 2016-03-09 09:22 .0 F08/0L9/02 O 1. (10 points) Determine if each of the following function is a parametrization of a manifold. 15. 12W nab/112 _/ _ (a) Villa—1:1) -> M given by 710:): (.-= I. d, Ella/“awe 01%” 005w) } 3" r5 INJCCT'Jvc (b) 72 : (—1/2,1/2) —%M given by ’72“) : (—sin(wt3))‘=: ND ' ‘7 PAWAMC' 2; 4"“ 5: .r. «'léyi Elim- 01” MAMFoLp l6 7, BUéc/Tivé Wm) - guﬁjv’EGflVE :ﬁnrrc \j LE?” ’ l, 6 M ix :-+ ‘7 AT Léflé’r aNé NOT 0 /" yéﬁw" W/NJGC’TIVéﬂSlA/G'TZ’;ON€> r, _ f- 91(5)?— 919‘) =- 35”; g _ j ég j; =‘ 6 All“)?! ‘rﬁt‘l l y (-79 ‘6 @‘KQﬂﬂlwlfﬁ g1 lug ? Mk 9mm '14 m.” (12111 B 1412a“? 9%“ 13 1Q: . > [DE/:14"? 7/ "w'i J ———- ETQ um r ,. “’ 'é’W 7;; We} Elk r’ Isiwémué -— Slugger-um +5 (N ICC/“ﬁve? grim”; ’ IBIE—Fdos‘lfjk ' 2:60: 2163 V64 A'r' Lé/lé'r’ jg =— <5 - 0H5: WF‘ 96% iGraderOnlyJ, I O® @@@@@®@®@® Q O. F08/0L9/0L . J points) Let X0 = { 3:3 + y3 — 31,! = 6}. Determine all values of c which make Xe a smooth curve. 3/ ‘K. E- a , F- _.‘ ,— Jr \/ F— iﬁ, T: /1_H__‘ x7, /" / L x r f / w I 1/5,, :7 ___\I #7 fy i ﬂ 'v/ "i 1?: L'L_,r—>4 a‘— 11 / ﬂ / é/ “w” l: r I; f f f T7” fur-g; ~11: {\ if: ‘t x. ’3/ Q 1/ — ’F 7 k“ I "7%., .7 — j i c:- b *- j—( a H :- H_m _ f\ H_ _ t _ L V» —— ask-“x. a 15m; except C: i7- . Yeﬁ are EMA. J. Grader Only .1, O. F08/0L9/04 . 3. (10 points) (21) Several level sets of a function with signature R2 —> R are plotted. Foréanotted level set: determine if 1 smooth manifold. air/,3 , W (b) Several level sets of a function with signature R2 —> R are plotted. Plotted level set, determine if it is a, smooth manifold. /" / W (c) Is the following a smooth manifold? State your reasons- 1.5 l // I. -' NO Dre” rue-r ’ 1 - u) x/ J 3.5 -O.5 -1.5 - — -2 -1 0 1 2 lGraderOnlyJ, I O 069 0 ...
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