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worsheet 11 - Math 200 Spring 2010 Worksheet 11 Name KG...

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Unformatted text preview: Math 200, Spring 2010 Worksheet 11 Name KG; Section 14-3 Partial Derivatives 1. Find the first partial derivatives of the fiinction f (x, y) = x4y3 + 8x2 y . 3 "12)! (XI?) : [+3 731-15)”. 31‘- a 'lxlli‘)‘ EL?“ ': tf{q‘)-} +16(1-i):32+32:é|r J 3. Compute the partial derivatives of z = 3-C- . y A. K _L g ‘ )— _ 3 -- : ._. JS .. .3— ‘_ - _ 3"" 7M" r , 37(7)”)‘91'7' :3 4. Compute the partial derivatives of z : J9 — x2 — y2 . 3.0—“ _. l q__ 2__ a. ._ _ _ _. X 9* x v 2W1 1x)- WWW A {*1 z _ l I)" ll-X—y "' 2m (~2Y3 1-. -— V 5. Find the partial derivative fx (2,3) for the function f (x, y) = arctan(y/ x) . 4M”) _ \ A155) 3 \ (“7%") = xfj—T "— _ %_5 ww- 2* Her .1 I) 3 _..__ So 4:3:(73) 3 —' 21:”: " 1:3 6. If f (x, y) = 4 —— x2 —- 2y2 , find fx (1,1) and fy (1,1) and interpret these numbers as slopes. Illustrate. ( We (31-01% 0-9“ and “we. (lane ya] intersects uh +ke parabola; 2: 1~xL‘ The Slope 0'? He heated lim_ +0 +9“: umbala. 04—1119 Poiril' (1,1,!) ’.5 (MUS-.1, Tim Plug 7::1 Inlet-Sick iLe emulate 1.: Jane Pmelwla 2 x a; = 1—9 " and He shape «rt-WWW“ "lunahqi 1.7ae’ «'1' (MN) I'5 £70..” =-"f. 7. Find the first panial derivatives of the function w 2 2e” . Qua _ kite 3‘- X E “A"? : ae"”(x7)+—e""‘ = mam“? 8 Find 62g tfg(x,y)= "y . 6x x—y 2. 3 _ 2 __y_ .. 1i)?- - -I) __ x fit >137(x7) X (3P7): (x-;)1 '2. L. 1 L 3.1 A as, , a A , “(Pg-)9 [ax—AL 2m. 3— —x1 320) 3% 37) ' him?!) (#717 ' (X-vl“ :1 "£11., (fir733 9. Find all second partial derivatives of the function f (x, y) = x4323 + 82:2 y . 1 3~:? ”in : iifiixfiri‘r 3117)) z 3‘); (‘txygfl‘xfl : ”"7 + ”’1' 3 J _ 1 2. 1X) = :5); :33): (Kilian—17)) 3 '3, (“txy‘tlét‘fl - 12%; Hey «~— 3 1 A ‘1 ‘- L .. t1 . ‘i‘yy: %7L%}(X17+8X7)3 37(3xy'f3x) ‘ 637 92“,“! Stn‘ce ‘i: — A (2‘{ H 3 a a. -— A '1 1' L 3 1- deli-163?: 7“" By 97 x7+ ”7”“ 3x(33}+3x)312x7+l£)r <_ GNfoiit‘nmJ 10. Choose the order widely to calculate the derivative gzzwx, where g(x,y,z,w)=x3wzz2 +sin[fl;—]. ‘ t . A z Di%rtnd-Q+€ w.r.'l:. b6 'S‘H'S'l' a“) : J‘U xgwl-g-‘t- Sn; (3%)) :2 L22. P 3 1 3 44% 3mg: ;(wai) 54mg} 3 flwii :§%2(L+Xag):uz7w 3 3)"lz ‘ - (“VJ awe-h = ”(we 7 x” "3%4wv . 6211 6211 . . . . 11. The wave equation :3—2— = a2 6—2 1s a PDE that describes the motlon of a waveform, Wthh could if x be an ocean wave, a sound wave, a light wave, or a wave traveling along a vibrating string. Show that the function u (x, t) = sin (x ~— at) satisfies the wave equation. “x = WWW-at) LMm : ”5'3 (X_“fl .— 'L “H: _ ~C~COS (X-a‘f) la.“ 7' —a Sih(X—1t):QQ—L‘ny 31H _ L iii; ”We Tf“ —a 3x2. Homework #11 Reread Section 14.3 (Due 3/5) Do Section 14.3 Exercises: 13 — 27 (odd), 39, 41, 43, 46, 53, 57, 61, 63, 65, 71, 74, 76ab, 79 Prepare for next class session: Read Section 14.4 ...
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