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utions for sid - Google Docs Х M 2020SU-MATH-2415-19530 (Cal X + /?tab=rm&ogbl#inbox/FMfcgxwJXCFxKtjbJGbfwRz5fNjgXGrM?projector=1&messagePartid=0.1 nas Outlook Bb TCC - Blackboard W Cengage WebAdvisor Main... Calculus III - Googl. of and av of Use the general chain rule to find ди 3. Given f(x,y)=e" tan y where x=u+2v y=u/v leave the answers in terms of x, y, u and y. You may с 4. The temperature of an object is found to follow the function 7(x, y, z) =- where c is a x² + y² + 2 constant. The positions are in feet. At the point (1, 2, 2) the temperature is measured to be 120° F. What is the value of the constant c? If you move from the point (1, 2, 2) to (2, 1, 3), what the rate of temperature change? I 5. The electromagnetic field for a particular area is given by F(x, y, z) = xyer+z-s. A sensor is placed at (1, 3, -2). What is the direction will the sensor detect the greatest electromagnetic change? You do not need to find the direction cosines. 6. Determine the max/min/saddle point(s) for the function f(x, y) = x + y +1. Quiz-11-Keys.pdf Removed Solutions for sid.pdf pageeeee8.jfif pageer

Answer 1

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(u du Cytany) rutany • 1 t elytany, et tany. 1 du V > The Gq 2) = Sol 2fGx,y) = xy tany ) = exytany where Sa=utar { y = u/u df af ax t of dy du dx du af = a (erytany alutav) + (rytany a du da du dy Ixlysecy rytany Cytany + xysecty + xtany du of = df. dx + df dy du da dv df = alexytany alut20) tal paytany). du dx do dy dulv lytony) e tytory, a terything xlyseży + tany euf- edytany (Qytany #- Lysety - stany bol.4 vx²ty²t2² At (1,2,2), T = 120°F Sog 120 = =c 1²+2² +2² C=360 Therefore, Tl, y, z) = 360 x²ty²+2² 4 (2,1,3), T=_360 = 360°F 12+12+32 AT = 360 120 Ar (121)741-2)²+(3-2)2 W3 do df du 1929 Wh

260 - 120 A dal Fy = af dé OL = Ar SI -13.732°F (feet 122°F (fect ²+2-5 Sol 5 F Gg , 2) = xye Fx = af y others to 425 10x425 dy F2 = SE = xye the point with field be (7) 2+ly-3) 24 (2+2) ² = R² Ø (x, y, z) = +(2+2) ² - R² day, 2) - xty² + 2 - 2x x-by +42 + 14-R² OF + dod=0 x+2²-5/2x² H) + x (2x - 2) =0 22-5 522 d2 Let Grote greatest electoszregretic dd д de + ddo da dy Xe 772 - A Cay - 6) =0 yext T DE todo =0 dz dz x²7z²5 axyze '+x (22+4)=0

Sel 6 fly) p= fx = af x + y + 1 (y=ol q = fy = af My² dj r = fxx = of = 120² da2 fry = t dz 12y² 2 There is 80 2 >D=9t -5% = (122_)(137) 199xy no value of Dco [no saddle point , critical point logo) Also r=0 & more investigation needed that f(ngy =0 tot 1 2 So We can see at lood minimum abe There is no local moxina so global maxima is 100