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Vzx fbyj cxg. E i ԍ hgs0002 E i z _ i @ I v ` F P X t Z b g i c @ b h/R110 j. Answer to Find ∂z/∂x and ∂z/∂y (a) z = f(x)g(y) (b) z = f(xy) (c) z = f(x/y). 352 Chapter 14 Partial Differentiation k;.

F B Y j R X ` A C ɂȂ ܂ 񂩁H y ȃZ b g z t @ C u X ^ v Z X h X V f E h Z b g p j G A e B A y y M t_ z yHLS_DU z y h X R X ` f B Y j v Z X V f L b Y q ǂ P l 킢 X e W V Y q p disney z I X X x. The partition theorem says that if Bn is a partition of the sample space then EX = X n EXjBnP(Bn) Now suppose that X and Y are discrete RV’s If y is in the range of Y then Y = y is a event with nonzero probability, so we can use it as the B in the above. For three variables, a level set is typically a surface, called a level surface EXAMPLE 1415 Suppose the temperature at (x,y,z) is T(x,y,z) = e−(x2y2z2) This function has a maximum value of 1 at the origin, and tends to 0 in all directions.

F1 S ꗥ\1,100 y5kg T C Y F4 U ܂Łkg T C Y F6 U ܂Łz o 肨 q l ̂ v ɍ i 񋟂 ƍl Ă ܂ B. T h e A d v e n t u r e s o f T o m S a w y e r i A F e w W o r d s t o B e g i n M OST OF THE adventures in this book really happened One or two were my own experiences. Evaluate the surface integral ZZ S xyzdS, where Sis the part of the sphere x2 y 2 z 2= 1 that lies above the cone z= p x y Using the spherical coordinates, let us write the parametric equation as.

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For the best answers, search on this site https//shorturlim/avVky put x= 0 f(x) = d = 2 put x = 1 f(x) = a b c 2 = 5 or a b c = 7 put x= 1 f(1) = a bc 2 = 3 or a b c = 5 add the 2 above equation to get b = 6 and a c = 1 so f(x) =a x^3 5 x^2 c x 2 put x = 2 f(2) = 8a 2c 2 = 4 8a 2c = 14 2a 2c = 2 subtact to get 6a = 16 a = 16/6 b =. Get 11 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator. E 6HNLVXL RXVH /WG ª ø ) y h V ¥ d k z 4 B V 4 j C f É C & 2 q J } 4 a ) 4 B V 4 j C Ä g V z 616.

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MATH 215B SOLUTIONS TO HOMEWORK 1 3 4 (8 marks) Given a space Xand a pathconnected subspace Acontaining the basepoint x 0, show that the map π 1(A,x 0) → π 1(X,x 0) induced by the inclusion A,→ X is surjective iff every path in X with endpoints in Ais homotopic to a. I ` ̂Ƃ @ @ ɓ G q ΐ쌧 s 7 d b F @ e ` w F. !b#b#H * * * $ !b# !b#S * $S * *B o k b# N8b?.

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