Sw (a) Given w(x, y, z) = 2xyz,x = s² + t², y =, and z = In t, find and 8s Sw St

Q: If z = e'x + y In(x), find z, and z, Zx Zy II

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Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT> XT. Y

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Q: if f(z) = (ax – x³ + 3xy³)+ (by – 3x²y+ y') is anal ytic , then the value of a and is

A: We have , f(z) = ax - x3 + 3xy2 + iby - 3x2y + y3 We have given that ,  f  is analytic function.…

Q: Given: WX 1 XZ, YZ 1 ZX, WZ = YX Prove: ΔWZX ΔΥXΖ Y W

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Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

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Q: Given, f(x, y, z) = xln(x?y)+ x*y – e a2. Compute fa, f, fry, fayz-

A: If f(x,y,z) is a multivariable function, then the variables x,y, and z are called the input of the…

Q: Given w = xysin(z²), x= s-t, y = s², z= t². Find ay

A: Explanation of the answer is as follows

Q: o Find the Vf at the given point 1.f (x,y,2)=x² + y² -2:2 +z In x,P(1,1,1)

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Q: The identity LiS L xyzdzdxdy = "/2 S Sa rsin@cose zdzdrd® x² +y² 1-y² x² +y² is

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Q: Determine if the nontsivial Soluton ystem has a X,-3>c + 7)C3=O -2x,+ Xz -4x3=0 923=0 Xi + 2x2 +

A: To determine if the system has a non trivial solution.

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: (3) Derive ACFS Pk, k = 1,2, ... for the following models. (a) Xt = Z¢ – 02Z¢-2 (b) Xt – 0.3Xț-1 =…

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Q: (a) (x² + y² + z² + w?)3/2 = 4

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Q: Given F(x, y, z) = (z, x, y) Solve for: а) divF b) curlF

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Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: Sw 1. Given w = xysin( z?), x =s-t, y = s2, z = t2. Use the Chain Rule to find St

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Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: Let  z=xln(x2+y2−e4)−176xy, x=tes, y=est.  If the value of    ∂z ∂t   when  s=2 and t=1  is equal…

A: z=xlnx2+y2-e4-176xy x=tes,     y=est use the chain rule to find the partial derivative…

Q: 1. Let T1,T2 : R3 → R² be given by: T1((x, y, z)) = (3x – 2y + 5z, x + 4y – 7z), and T2((x, y, z)) =…

A: Solution is given by using the matrix representation of given transformation as

Q: In the given figure, X > K. Prove that WY> JL. K X Y W

A: Here , we have ∠X>∠K we have to prove that WY>JL

Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: 2. Find Df(x, y, z) for f(r, y, z) =x In z+r+ y at (0,0, 2).

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Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: If T = x' - xy+ y', x = pcos 4, y = psin ø %3D Find a) - ôp ƏT b)

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Q: If F (x, y, z) = xyzî – e² cos xĵ + xy² z³k, what is V · (V×F) (1, 2, 3) 1 2

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Q: (x + 2y), 0sx<1,0<y<1 fx: 0, elsewhere PG<x<를 &y<b a.

A: Given,f(x)=23(x+2y); 0≤x≤1 , 0≤y≤10; elsewhere

Q: If f (x, y) = V3 + y³ In (z +y°)e*in(zyty") +2² + 10y , then fz (1,0) = |3D %3D O 2 4. O 3

A: Given that fx,y=x3+y33lnx2+y2esinxy+y2+x2+10y3 First we have to find fxx,y where fx=∂f∂x

Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (a) z = x2 - 2y2 ; x = 3s + 2t, y = 3s - 2t

A: It is given that,            z = x2-2y2  ;  x = 3s+2t  ;   y = 3s-2t We have to find  ∂z∂s  and…

Q: Exl Let c R,Z) be usual toP s Pace and A-fcxy)ER/ x²+y²< 13 find A Ext CA), Ā , A°

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Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: ( a) 2.xdV where E = {(x, y,z) |0 < y < 2, 0 <xs/4- y² ,0 < z< y } E

A: As per Bartleby's answering guidelines, we are supposed to answer one question if more than one has…

Q: If w = e" + v², z = u³v+ 2ve", u = x2 - y?, v = 3/xy Find a(w.z) a(x.y) at p(1,1)

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Q: For Z= x²csc y,prove that Zxy is equal to Zyx

A: Given that,    z=x2csc y

Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: W = xyz, X s + 3t, y = s - 3t, z = st? (a) Find dw/as and @w/@t by using the appropriate Chain Rule.…

A: As per the guidelines we can solve 1 problem only.

Q: | 2.xdV where E = {(x, y, z) |0 < y < 2, 0sxs 4- y²,0<z< y}

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Q: z=xln(x2+y2−e4)−176xy, x=tes, y=est.  If the value of    ∂z ∂t   when  s=2 and t=1  is equal to…

A: we have to partial derivative by using chain rule

Q: (a) The function z depends on u and v so that z = 2v(4- 3u)? u = 2x + 3y and v= 3x-2y az when x 0…

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Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

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Q: H. If g(z) e2*z In , compute g'(r). What techniques should you be using in this %3! case?

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Q: (a) z, and z4 where z = sin(2x) + y, x = s² – t², and y = s² + t² (b) z, and z4 where z = e*+y, x =…

A: We need to find the partial derivatives z.