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122test2ans - Math 122 — Test 2 Name A N3 W ER 3 Show...

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Unformatted text preview: October 20, 2011 Math 122 — Test 2 Name A N3 W ER 3 Show work for full credit. For each function, evaluate the given expression. 1. a. f(x, y) = 1/99 — x2 — yz , find f(—3,—9) b. f(x,y,z) = m/E 1n y, find f(4,e,—1) R2354,» : Jag — {—331 ~63? £01,6—, 4):-0J7? M 0. 21m ”’2 3 J7 =19, For each function, find the partial derivatives, fx(x, y) and fy(x,y). 2. f(x, y) = (x + 2y)'l 3_ f(x,y)l= yew may» = « 6+2in 5%va «Ru/7% 7 e12. gym/1 _— K ,‘l/L _2719}*7 2 0H fl 1C (W/ _ 51 QWHW 319ml (my) 3 ~ (MW? 337 (“+271 Y _ 62ml + 7 a“ : WEZW] 2‘87“? 4- 2xy 21:7 I Find the second-order partials, f”, fxy, fyx, and fyy. 4. f(x,y) = 3x2 — x3);2 + y5 QXCX 73 LE 2. Q. g‘cx’fldfl’fixy ' Mm: WV‘ V“ 7. L7CXI7I>Z ~2x37+ Syl‘l £7 70(7): :‘ beJrQOy October 20, 2011 Math 122 - Test 2 page 2 of 3 5.Find the total differential, df, of the function f(x,y)=1. : xh‘k/ x _ ‘2? 213 : ax‘zy Ax + {WW 2 clx + X&\ ’ “VAX 4" ii- : y L / x7. X X 6. Given the function f(x,y) = ye” +2x, and values x =0, Ax = dx = .1, and y =1, Ay = dy = .05. Find df using differentials. (Do not use a calculator.) At : {Ktkfl Ax + fyCK/fl AV —_ eye—x+/&,\ Ax + e‘xAy um mfl 40,0 wk (Ann/>404» 0'”) , it : meadow +01 W“) : Li\(o.|) + (’I)(O.o§> : [0.15“ Find the relative extreme values of the function. 7. f(x,y)=—2x2—y2+2xy+2x+4y—-5 o:£(x,fl:~’7'><+z‘/*Z :3 qX’ZY :3 .. 2 .2 , ; ’2 + 2x +Li W canal 90m: ngyflg, g} m; =x amhzyztl 27/:IO D : fpr 3:)“, — “Li 2- YZS ~2. {>01 £57 2 2.2-: L—{>O : (WM-23 — l . . GWX 55%;. S: Q5}S\:—¢-/<o / «£03,5—» 3 2 7— ($.th MQXIMUM . October 20, 2011 Math 122 - Test 2 page 3 of 3 8. Use Lagrange multipliers to find the minimum value of f (x, y) = x2 + 2y2 — xy subject to the constraintx+y=24. Lab Six/V): x+y_2_t7l I M L —?J-[ Fawn :mxmam: XWWKWMW ’ 0: FX :— ZX ‘7' +2 1% 2x..>/:L£7-><~ : ‘7‘ 0: FY : HY‘K+>‘ “K 3><=§7 “R Y:%X 0: FR :. X + 7‘2‘1 X+%X:2L{ .39 §5_x:zk{=> X=lb y = gm =3 7 = Cl m‘uniMuM valve :!¥(/SJ 93 =3 232, 3 L y 9. Evaluate J I 8xydxdy. 0 ( ) 85 My “7&7 SliCty‘w‘l'OL-YVV : ist'vi‘iv 1 Vila) : 520%: E] 10. The temperaturex miles east and y miles north of a weather station is given by the function f (x, y) = 60 — 4x + 6y. Find the average temperature over the region below. 5 a 3 all/Lt} {Jiix'fl (MAW ; 2': S L ((00 —’—{)s+éylecl7 K 5 Q. . t—(ijj @Ox—ZXL+QX\/\’ A7 2 o o h ‘3 : Zia/j QoD‘Z—Q‘ZL +9.27, - 0} A7 : {:8 (H’ZH’b/Xciy O - z, (“17+ WW :7: (“2.3 +5320) 0 3 ‘(95— (Lima! ...
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