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Assignment with Solution for Calculus III | MATH 210, Assignments of Advanced Calculus

University of Illinois - ChicagoAdvanced Calculus
Prof. Yun Guan

Material Type: Assignment; Professor: Guan; Class: Calculus III; Subject: Mathematics; University: University of Illinois - Chicago; Term: Spring 2009;

Typology: Assignments

Pre 2010

Uploaded on 07/29/2009

koofers-user-57
koofers-user-57 🇺🇸

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Math 210 Exercise(Q7) 3/6/2009 Name(print): Golectjon. Problem 1 (ts). Given [(«,y,z) = xe" and c(t) = (17,1? — 4). Use the . : d,, Chain Rule for Paths to calculate qi el) att = Q. cloy= ¢ 0.0) Arf fe Ley] = vfeiy CU]. 0 =. <0, +4> =<1,0> '€o0,-4) =o Problem 2 Ccts). Calchulate the directional dirivative of f(x,y, 2) = z?—xy? at p = (2,1,3) in the direction of: « The gradient. Puf (Pd = Iv fol] vfp = H<-gt 7244, 24] op iS ce -- Dif(p)= Jeegeay ee? SSB « The direction of v = (-1, 2,2). (Remember to normalize the direction vector). Duf (P= qa Pv FOP =a PEEP’ Y (2.1.35 2a Sohn 4 6 <-1),2,2> | ay Cin-3 te) a2 3 © The unit vector u making an angle of 8 = 5 unth the gradient. Def (p)=) vf pl cose = 553+ Cos JR