assig6sol - MAT 1322A Assignment 6 (Due Wed. April 8th at...

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Unformatted text preview: MAT 1322A Assignment 6 (Due Wed. April 8th at 8:30) Student Number: 1. Find the tangent plane to the surface 2 = so 1n(y) — 2m + 1 at the point (cc, y, z) = (3, 1, w—5) . work: 62m): zflfi-Ja-e/ =9 74;: '02, 6L: if yaw/91W m 2: flag; + flaw/94-41..» {gm} (7-4) ~S+ (Am _.2)[2c-3) + QM?» /) If t ‘5‘ ‘“‘ 07(70‘3) +3fg~/) t ‘5“ 42n+ 62743-3 Answer:lz= - Q1 -B? 5 2. Find the linear approximation of the function f (:13, y) = (my2 +5)1/3 at the point (2:, y) = (3, 1) and use it to estimate f (2.97, 1.02) . Work: jg : 7g : l(’172+5.)"g/} (‘9’?) L (91(3): 793”) + £01!) [2—3) + [31) [9-H = (3(‘:)’+5)i’3 + §€(3(:)‘#5)""’(“I)2/x<3) 4'3 bmjfflfi? (5/30))9") : 2 + it (79—3) «4- 33(214) . . ~ . .1 l , ‘ - {(297,},02) a L[.9.9'7,/.oa) : 52+ 75 {Q.?7»3)+‘9(/,</1 z) _ Q... 0.03 + £03 - ‘- 2 .. ,2 Answers: L(x,y) = Q 4- :3 (1.3,) +£(104) ‘ f(2.97, 1.02) z 3. Given that 'w 2: 1n(x2 + 23/2 + z) , :3 = tcos(23), y = it and z := t, use the Chain Rule to 7r find £92 and £92 at the point where t: 1 and s=7r. w/b?‘ at (98 )1, ‘3 ,2 Work: ‘) i=amfi+%§*az at ,, I ,_ 27L )‘Z—S— +( )3) “(zflzywfin (W) “251* ( ‘ _ a“; _ c); y g5?" 37? ds Jr 39} 5% “in M 2‘ a .21. _ _L = i ' 1+ L So ewww 0+ 9 .2 w - a . l)’: “3 ‘ (‘1)(0) *(w 7:) 8w 810 i Answers 197 79—8— = /n- . Bz 32 . . . . .. . . 4. Determme a; and @ 1f z 1s glven lmdlmtly as a functlon of x and y by the equatlon 902 +3162 = 23. Work: -:.>1 ' 5,1, A z .. A “3 : ' . ~ezé7= a 2‘29}é :5; (7L+Ie)—al(2) ) flit-Fa dh 3 dh Qn 322’ (92 Answers -~ = 8x ...
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assig6sol - MAT 1322A Assignment 6 (Due Wed. April 8th at...

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