Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 , 2iz1+(4-3i)z2 - 3z3 )

Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

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Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Verify that fy = fx, for the function f(x,y) = x° + 3y° +7. 9 For the function f(x,y)=x° + 3y° +7,…

A: The given function is fx,y=x9+3y9+7. Evaluate fx as follows. fx=∂∂xx9+3y9+7fx=9x8 Thus, fx=9x8.…

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: For the function f(x,y,z) = In (10x + 7y + 6z), find fy, fy, and f,.

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Q: Find the derivative of f(z)= In(z-+-3z+2i). O (A) ƒ'(2) = O (B) ƒ'(2) = O (C) ƒ'(2) =1 – O (D) f'(z)…

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Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: Find the linearization at x = a. f(x) = 6x®, a = 1

A: Linearization L(x) of function f(x) at a is given as L(x) = f(a) + f'(a)(x-a)

Q: Use the chain rule to evaluate fu and f, at (u,v)=(2,-2) where f(x,y,z)=y³+xz² and x=x(u,v)=u+v²,…

A: Concept: The chain rule for the function f (x,y,z) is  dfdu=∂f∂x∂x∂u+∂f∂y∂y∂u+∂f∂z∂z∂u…

Q: Let F(z, v)-v +y+3z+1-0

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Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: Find the linearization of f(r, y, z) = x + y² + z³ at the point (1, 2, -1).

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Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: Find the direction in which the function is increasing most rapidly at the point Po. f(x, y, z) = xy…

A: As a first step, we need to find the gradient of f(x, y,z)

Q: Find a point zo where the function f (z) = (z – 12 – 12i) (z – 12 – 12i) is differentiable. What is…

A: Given f(z) = (z-12-12i)(z -12 -12i)¯

Q: Find a point zo where the function f (z) = (z – 8 – 6i) (z – 8 – 6i) is differentiable. What is the…

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Q: The gradient of the functiong(x, y, z) = In a In y In z at the point (2, 4, 3) is:

A: Given, g(x, y, z)=lnx lny lnz

Q: Find the linearization L(x) at x = a. 1 f(x) = - x - a = 1 %3D -

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Q: The gradient vector of the function f(x, y) = sin(4x - 6y) is (4 cos(4x - 6y), 6 cos(4x - 6y)).…

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Q: Suppose F (x, y) = (2xe-", 2y – a²e="} (a) Find a scalar function f (x, y) such that F = Vf (b) Use…

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Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

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Q: Find the gradient of the function w = 2x²y – 4yz + a at the point (1, 1, -2). O 2i+ 10j- 8k O 4i+…

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Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Find a point zo where the function f (z) = (z – 8 – 10i) (z – 8 – 10i) is differentiable. What is…

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

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Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: The linear operator T: R2 --> R2  defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?

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Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: Find curl F if F(x,y,z) = 16y5₂5i - 8x³₂8 j- 7xy4k. O curl F = (-28xy3 +64x³₂7)i + (7y4 + 80y5z4)j +…

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Q: Find the gradient of z = (7x + 4y)e. Assume the variables are restricted to the domain on which the…

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Q: Verify that fy fyx, for the function f(x,y) = 3x° +4y+ +7. %3D For the function f(x,y) = 3x° +4y° +…

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Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: Q = find of るf and るこ for the Ganction f(xz)-ディズ メ+Z

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Q: Find the linearization of the function f () = z7 at z = 1. L (z) = 固助 Using this linearlization, f…

A: Given function is

Q: Find the domain of the function f(x,y)=V13032-x + y-> {(x,y) E R2 | y# x2 and ys 13032}. O {(x,y) E…

A: Given, fx, y=13032-x+1y-x2

Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (7xy + 13xz + 17yz)²]. O…

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Q: Find the derivative of f(z) = In(z -+ O (A) f'(2) = 2² – 3z + 2i). | --2 V:-3:+2; 1 AB) ƒ'(2) = V-3:…

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Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

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Q: Determine the linear approximation of f(x) = x* at x = 1. а. у %3D 4x - 3 O b. y=- 4 x - 3 О с. у-…

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: Let F(x, y) = <3x?y3 + y", 3x°y² + y^ + 4xy³,. %3D Evaluate F. dr where C is the line segment from…

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Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

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Q: 4. Show that the function f : X → Y defined by f(X) = X U {a} vX €x is a bijection.

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Q: Let f(x, y) = (x² +(3))°. Determine the directio %3D 4)

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Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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