Quiz3and4_solutions - 24.04.2008 MATH 120 SECTION 21 QUIZ...

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Unformatted text preview: 24.04.2008 MATH 120 SECTION 21 QUIZ — 3 Name: 50L”u'T\0NuS Surname: Id Number: 2 5 a 0,0 1)Let flxsy): x2+y2 f0r(x y)¢( ) 0 , for (x, y) = (0, 0) a) 13 f continuous at (0,0) ? b) Find 2}: at (x,y) = (1,1), if exists. I c) Find % at (x,y) = (0,0), if exists. 2) Let f :R —) R & g : R —> IR; be differentiable functions. Suppose that 2(x, y) : f (x+ ay) + g(x —ay) where a e R — {0}, Show that 2 satisfies the equation 4922” = z”. 7. x ‘ \) Q) “on $Kfit‘j) -.: “m ‘--—L—-—3__ :0 ang{ 1 bum—mom) Kx13'1—5kclo) % *3 2- ‘L. x 5 x as kn.3)—s,s.oo) 05* T: \T- ‘1“ 4-\::\-———————i——_»0 2“ j :3 \___,_.—..~_‘_—_) é:{ b3 Seqoeezg *Mfiorgm - S o, \{m $4.313) -_-_ 5900,10). ('x'fi‘] 'APLOJO) Tktct‘got‘fi Q- ;S Lot-{Yifiuous q): KQIQ). 3x 3x 11.31. HA) , lwkx‘fl‘Fxlj 7—K \ 1-\~{-U7'+\1')-i1-\«2-& \‘Kléfixul (9+9 3" HM.) —- (“—1 —J_ 1.. — 2. \n — Riva 0) C) E.— K‘OJO) = “m ngO’ 1 ‘ FPQVRAQA “\Mq’t 3:, ‘h—‘rQ Na *Mg \qu-‘c exis’rs. "L 0 \n 4KOJOH=Q Sivan. {:KOAO: L =0 0 Mn“ --?LO.<>] 0—0 50, “m {:Ko'k) _ = “m :0 TMEPL$Q¢EJ 2"? Lc,o) :20. 3:5 7-) 2x: $‘KK*Q5)- ‘\ 3r 5\\**°\“3\'\ 23: £‘Lx+o~33-a +3‘Kx-a‘3) V“) 2,“ -. €"kx+a3)-\* 3“ \xmij 153 : 43“ kx*q3§-Q1 -\- 3“\r~.-Q~3) K—oql : 611' [$“kx-\'Q5) "r 5‘\Kx-q3)] = a?“ Z“ 01 .05 .2008 Math~120 Quiz-4 Name? SQLU'T\QNS Surname : Id Number : Questions I) Find all points at which the direction of fastest change of the function f(x.y) =1:2 +y2 —2x—4y is < 1,1 >. 4 2 3 . x - 2) Compute jjsm [?_x]dxdy 1J3 - n The, Air-edition 0'? ¥q5-\c-_s-\- cincmae, {.5 in 'Hwe. same. Airtc’d‘on as V$=<$x,¥37=41x‘1J7—3‘L§7 So, 41, \‘I one 42.x—l,2‘3-147 0.99.. in i419. scorn?— éicecHan. [<\.i‘> //L7.;<—7_,2.3-l+7) Tints rs .sofirtsPraé. 0q\3 H3 2x—1:23—L;. ér 2x-13-\-7_:.Q of." x—ji-kzo Hence. *ke. Aes‘weé {Baird's ave Hue. Poch-s On “the! \ine x-j+t=o. Or we. Lam Ot\.s<a Sq: JrkL Aashrgé Poin¥s SQ‘N‘LS‘CJ 1X*'L-:.'t cmA LE'Lizt =9 'i'kc. Pair-{is cu??- (XII): L %(t*111%(t*q)) Vtem- fink, 1‘? X=k "flntn U: -— I 3 Thara¥oce_; 1 —3 7-13 Sssan—i—dfi)éfi= SS\nUAU:—C_O.su 0 Hi i 3 3,. ———Lo53:— —- (—L05[1§—))_ —c,o$—%—+ LQS}§~=O ...
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This note was uploaded on 05/09/2010 for the course MATHEMATIC 120 taught by Professor A during the Spring '10 term at Middle East Technical University.

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Quiz3and4_solutions - 24.04.2008 MATH 120 SECTION 21 QUIZ...

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