Find & for f(r, y) = y- 4ry + 5y .3 2

Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: f(x, y) = Find fx, fxy, and fxyx. 7 8x+5 + 8x³ e-8y

A: The given function is;  f(x,y)=7/(8x+5) +8x3/e-8y.

Q: F(x, y,z)= (4xyz) î + (-2xz+2yz) ĵ -3y² z k , find VxF

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Q: F= [y°, 2², x²], C : r= [3cost, 3sint. 2t], 0 < t < 4n

A: Given that F=y2, z2, x2 and the curve, C, such that, r=3cost, 3sint, 2t for, 0≤t≤4π. Differentiating…

Q: f(x, y) = x + y' subject to x + 4y = 29 occurs.

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Q: 2x-y if F(x, y) = xy é e af ар ay ах find

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

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Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: dy If y = V2-x, then find de 10. A 2-x 1 В 2/2-x 1 C 2-x 1 D 1.

A: Given y = 2-x we have to find dydx.

Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

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Q: For F = (3xyz^2,y^2sinz,xe^(2z)). Find ▽⋅F and ▽xF.

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Q: For Vx 3 evaluate y when y = 4. 2

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Q: f(x, y) = 2y – 6ry - x 2.

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Q: Q1/ If z = f(x, y) and z* - y? = 6x²y°z7 Find: and dz

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Q: Ifx' +y +z -2aņz =1, then show that V1-x dy 1- y V1-:

A: We have to use the given condition x2+y2+z2-2xyz=1 to find this.

Q: V = f(x, y) = x²y ,x(t) = 2.

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Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: ∆ XYZ ≅ ∆ PQR, XZ = 3y – 7, PR = 2y, RQ is 25 less than 3PR. Find y, XZ, PR, and YZ

A: Given: ∆ XYZ ≅ ∆ PQR  XZ = 3y – 7 PR = 2y RQ=3PR-25

Q: Se-2t if 0 3,

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Q: Given f(x, y) = - 5a4 – 4x²y³ + 6y°, find - fa(x, y) = fy(x, y) = %3D fez(x, y) =

A: As per our guidelines we are suppose to solve only first three sub-parts of a question. Kindly…

Q: Suppose that W (y1, Y2) (t) = 4, and y3 Yı – 3y2. What is W (y1, Y3) (t)?

A: Correct option -12 We have to find out the value for Wy1,y3t.

Q: If f(x, y) = V + y3, find fy(0, 5).

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Q: f (z,y, z) = x² + y² + 2² subject to zyz = 4

A: Given: fx,y,z=x2+y2+z2 subject to xyz=4 Let gx,y,z=xyz-4 Using Lagrange Multiplier fx=λgx, fy=λgy,…

Q: Given that x= 3y and y = 2z, find x : y: z. %3D

A: Given x=3y , y=2zx=3y  =3×2z  =6zthe proportion x:y:z=6z:2z:z         =6:2:1×zdivide by z , we…

Q: f(z) dz = 4, then 2f(x) – z dz 13 If %3D =

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Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

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Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: Find fr, fu, and f.. -0.5 f(x, y, z) = (4x² + 6y² + 3z²) fz = fy = f: =

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Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: F(x,y, z) = 5x² + 2y² + 4xy + xz

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Q: What value of c will satisfy y(x) = c(1 – x²) given y(2) = 1 ? %3D ) Option 1 Option 2 2.

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Q: Q3: 1f f(x, y) = 4xCy5 + 6x*y* .Prove that: f(x,y) * fxxyy fxx * fyy = 1

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Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

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Q: Find fxxy given that f(x, y) = e^xy^2

A: Given,   f(x,y)=e^x *y^2             we have to find fxxy

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: Find y' for x^2y^4−3x−3y=13 at the point (−1,2)

A: Given Data: Equation: x2y4-3x-3y=13 Point: x, y=-1, 2   Differentiate the above equation with…

Q: f(x,y) = x² - xy +y² – 9x + 6y + 10

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Q: Sove the IVP y" + 2y' + y : if 0 4

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Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: f(x,y) = 3y3 – 2xy + 12y – 3x² – 8x – 16 then fy equals ух

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Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

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Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

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Q: Find E[Y(z)] when Y(z) is given by 2z' + 6z² + 5z + 1 2(2z + 1)

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Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-