ALet f (2) = x² + iy² where x and y are the real and imaginary parts, respectively of z and C is a contour consisting of the line segment from z1 = 2i to z2 =7+ 4i Evaluate Re [f (z2)] ?

Q: Let f(z) = x² +iy² where z and y are the real and imaginary parts, respectively of z and C is a…

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Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Find the exact value of Duf(-2,-1,-3) in the direction of v = 3i+ 4j + 5k for the function f(x,y, z)…

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Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

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

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Q: Suppose that f(x, y) = e-2r² – 1y² + 2x +8y then find the discriminantD= faz fyy – fay- Question…

A: Solution: The objective is to find the discriminant

Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

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Q: For the function ex, the linear approximation around x = 2 is %3D

A: Introduction :

Q: Determine whether X and Y are independent: 2e--2y x, y > 0 a. fxy(x, y) =

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: Use the linear approximation of f(x) = /2x - 3 about c = 2 to estimate the value of V1.32 Enter your…

A: Given that: f(x)=2x-3

Q: Differentiate the function. y = In(16 + t – P) %3D y' = 1– 3r² 372 6 +t-t -- 6 + t- r 2 6+t-t

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Determine the linear approximation of f(x) = x² at x = 1. a. y= 2x +1 O b. y = 2x - 1 O c. y=- 2 x-1…

A: Given: f(x)=x2, x=1 To find: Linear approximation at given point.

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

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Q: a. Find linearization of f(x) = Vx +1 at x = 7. b. Using your answer above, estimate V8.1.

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Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

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Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

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Q: Let f(x,y) = ax + by2 af where a and b are constants. If of at x = 1 and %3D ху y 2, then the…

A: Introduction :

Q: For the function f(x,y,z) = In (7x+ 2y +5z), find fy, fy, and f,. fx =口

A: Given,           fx,y,z=ln7x+2y+5z

Q: Suppose that f(x, y) = y/x³ + 1 at which {(x, y) | 0 < y < x < 1}. %3D D

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Q: express in the form y = f (x) by eliminating the parameter x = t + 3, y = 4t

A: The given parameters are x=t+3, y=4t. The objective is to express in the form y=fx by eliminating…

Q: Let f(z) = x? + iy² where æ and y are the real and imaginary parts, respectively of z and C is a…

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Q: For the function f(x,y,z) = In (6x + 7y + 4z), find fx, fy, and f,.

A: Given: f(x,y,z)=ln(6x+7y+4z)To find the fx, fy, and fzddx (ln x)=1x

Q: If f(x, y) = 8xey + 8y Inx, then is given by:

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Q: Let f(x,y,z) = x2yz4 + 4xy²z+y²z - 3y³z Find fxyz

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Q: Determine the linear approximation of f(x) = x° at x = 1. a. y= 8x +7 b. y=- 8 x - 7 C. Not in the…

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Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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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: function f(x, y) = 2x^3 + 6xy^2 −3y^3 −150x has four stationary points, find

A: Please refer to the image below

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

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Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: Let f(z) = x? + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

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

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Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Find the absolute maxima and minima of the function f (x,y)=2x²-4x+y²-4y+1 on the closed triangular…

A: Given:The given function is f(x,y)=2x2-4x+y2-4y+1 on closed triangular region bounded…

Q: Let f (2) = x² + iywhere x and y are the real and imaginary parts, respectively of z and C is a…

A: The given problem is to find the value of Re[f(z2)], where given z2 = 8+7i and function f(z)=x2+iy2…

Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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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: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

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Q: Let f (z) = x? + iy'where x and y are the real and imaginary parts, respectively of z and C is a…

A: Real part of f(z)

Q: For the function f(x,y,z) = In (5x + 7y+ 9z), find fx, fy, and fz.

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Q: Let f (z) = ² + iy² where x and y are the real and imaginary parts, respectively of z and C is a…

A: Real part of complex number

Q: Calculate Duf(0,–2,5) in the direction of v = -3i + 12j – 4k for the function f(x,y,z) = 3x² + xy –…

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Q: Found the line of differentiability of f(z)=x2 - 2xy + 3y + i(2xy - y2 +x)

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Q: Is g(x) = Vx + 1 differentiable or not? Justify.

A: Note :-  f(x) is exist only if f(x)≥0.

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

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Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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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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