{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test2sol - University of Waterloo MATH 237’ — Calculus...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: University of Waterloo MATH 237’ — Calculus 3 Short Test 1 — Fall 2006 Version 2 Sections 01, 02, 03 Date: January 24, 2007 Time: 5:30 p.m. - 6:20pm Duration: 50 minutes , NO AIDS PERMITTED N O CALCULATORS ALLOWED Family Name: M Initials: __ Id. Number: Signature: Instructors: C] 01 L. Krivodonova {:1 02 R. Moraru D 03 B. Ingalls Instructions: 1. Complete the information section above, indicat— ing your instructor’s name by a check-mark in the FOR EXAMINERS, USE omy appropriate box 2. Attempt all problems in the space provided. If you require more space, use the reverse s1de of the pre- vious page. 3. Marks will be deducted for negligently presented work. Your grade will be influenced by how clearly you express your ideas and by how well you organize your solutions. Justification should be provided by referring to definitions and theorems where appro- priate. 4. This test has 4 pages. 1. M O l‘“ {(1,0) 2 5:30 ’32? (a) Verify that the function has no limit at the point (0, 0). I; 1‘1 "W fix 0 = "‘ "‘2 X40 I X40 17‘ Page 2 of 4 (b) Let 1: = 2—537 ($,y)#(0,0) 9(a) {L (55,9):(050) i) Find a value of L so that g is continuous on the plane R2. 5‘.an a U raj-Md 1'" ‘IJ Oo‘vJ‘ii/luuuf 5% a.” lamb [A {‘ltf 3‘ (Lemma féWraWLlr-V- €3<¢I7¢+ pal? (0(6). . “M L _ I Aflonwakiwg (0,9). alum; 7:0 ) \-Q ‘FU‘A 1 — Oi 3 Sinai we dirk +011 +1; (Mi)? exiJ‘H, we prune] 41 vent? W H1 [land {3 111m: 1 .231. \‘ -_— lxi “’¥‘ml in+71 10— 35%), = £ Ix. a! 171) 5 llxl'fijL! Sina hm 1*130 H4 Squeek WW M‘A‘rwf (mfieaw) ) W “H: limit LI 0. SQHU‘U L30 HIUHJ in ' I % \J’l‘NJ Cax+2nufius A71 (016), i ii) Is your answer in part (i) the only such value of L? Explain. (OVEN/‘43 03" (0,0) regutr-CJ W +Lz VILLA of ) iJ afiL/wl +0 ‘Ffil lim‘f. 5mm ‘H4 [Ind 15' 1-04 L WWI“ LE 8?!ou 4-2: 3.2m. 010:!) I “lam-1L3 L Page 3 of 4 2. (a) Consider the function u(a:, t) = 008(5): + at). By taking partial derivatives, verify that the function u satisfies the partial differential equation Bu Bu _ = a— at 81: ' ' - '2 U6 '[flvul 93%: = 51 C41(¥*4{) s . If t * Sin (7c +a{) 3t (X+A“\ : -a m (W10 “VJ "i": : —- fin (x+4+3 531(5‘4-“0 If : ~5in (7‘+a{.) W a 23%: : 3% AS require/X. 3’ (b) Find the equation of the tangent plane to the surface 2 = $2 + 3331; _ y2 at the point (9:,y,z) = (1, 2,3). Vi‘l'ix {($30 : 7(1-6 3X3 “‘31 i N 7. M +W‘11 '3: :11-43? “ML (‘3'? : 35(‘27 TL“ glhn=2+é=8 ) 9;:(I,1)=3—L/=vll figl f0 H1 ‘iMa-ei Fiend. ‘l‘ 1': 16“,?» 07+ (’11,?) Page 4 of 4 ...
View Full Document

{[ snackBarMessage ]}