Cutting the graph of the function f(æ, y) = x² + y? – 2x – 4y + 9 by the cylinder a? + y² = 4, we get the blue curve. Let (C) be the projection of the blue curve onto the plane Oxy. Then in the three dimensional space R*, we have (C) = {(x, y, z) e R³: z = 2² + y* }.

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = xy + yz + xz…

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A: As per the guidelines of Bartleby for more than one question asked, only two is to be answered, you…

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Q: . "Hand-in question": Find the extremal y € C²[0, 1] of the functional J(y) = (2x + (1/)²) dx, that…

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Q: 8. (a) T F The xy-trace (on the xy-plane) of the surface x² + y² − z² = 0 is a point. (b) T F If…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: (a) Find the solution of the limit using polar coordinate system. x² + y2 lim (x,y)-(0,0) x2 + y?…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Given: y1=t+10 ,y2=sin2t ,y3=cos2t

Q: TEANUCOGl b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz = 0. he

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 6x + 12y+ 18z on the elipse…

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Q: Study the analytically of w = L_r(z) at the points z = 0, z = v2,z = -2i

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Q: Find the linearization z = = L(x, y) of the function z = f(x, y) = 3.x2 – y² + 5y at the point (xo,…

A: z=fx, y=3x2-y2+5y and the point is x0, y0=2, 1. Now, f2, 1=322-12+51=12-1+5=16 Now partially…

Q: 4. Find f such that F = Vf and use it to evaluate SF. dr. (a) F(x, y) = (3 + 2xy²) î+ 2x²y ĵ, C is…

A: (4) To find: f such that F→=∇f and To Evaluate: ∫CF→·dr→. For the following Functions: (a)…

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

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Q: 3. Let R be the region below bounded by the parabola y = 4x² and the lines 3x - 2y +3=0 and y = = 0.…

A: Follow the procedure given below.

Q: Find the maximum and minimum outputs for the function f (x,y) = xy – y² on the portion of the disk…

A: The given function is f(x,y)=xy-y2    ....(1) Let g(x,y)=x2+y2-1=0    ....(2) h(x,y)=x+y-1=0…

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Q: (a) Evaluate f. (sin x + 3y²)dx + (2x – e-y*)dy, where C is the boundary of the half-disk x² + y? <…

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Q: 48. Let f(x, y, z) = xyz + 3. Find an equation of the level surface that passes through the point…

A: Given that: f(x, y, z)=xyz+3

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Q: 3. Solve the Laplace's equation = 0 dx2 dy? d22 in a three dimensional box 0 < x < L, 0 < y < H, 0 <…

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Q: a) Find the maximum and minimum values of a function F(x,y,z)=8r +y +z on the surface +y'+z=18

A: Step:-1 Given that  Fx, y, z=8x +y+zx4 +y4 +z4=18 ----(1) Take gx, y, z= x4 +y4 +z4-18 Using…

Q: Find the local linearization of f(I) = 1/1 at-3. %3D Ls(z) =U %3D

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Q: 1. Sketch each curve in the z-plane, and sketch its image under w = 2². (a) |z1|=1 (b) x = 1 (e) y²…

A: We are authorized to answer three subparts at a time since you have not mentioned which part you are…

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A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: Find the local linearization of f(I) = 1' at-4. L(z) = 0 %3D

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Q: 11. The y-coordinate of the centroid of the solid in part IV is.. A. 0 В. 1 С. 2 D. 3

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Q: O B. L(X, y, Z) = -7X-7Y-3z Find the linearization of the function at the given point. f(x, v, z) =…

A: The detailed solution of the probelm is given in the next step.

Q: Find the linearization of the function at the given point. f(x y, z) = e5x - 3y - 6z at (0, 0, 0)…

A: Linear approximation in three Variables

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Q: Consider the function: f(z,y) = 1 – xy coS TY (a) Find the linearization L(x, y) of ƒ at (1, 1) (b)…

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Q: The curve C is the is the positively oriented simple closed curve that maximizes the value of this…

A: Consider the provided question,

Q: Find the absolute extrema for f(x, y) = (x² + 2y²)e-x²-y' over the closed disk D: x° + y° < 4. 2.5 2…

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Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: 5) Let R(x, y) = 3x² + y². Find the minimum value of R on the hyperbola xy 2.

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Q: Find the linearizations L(x,y,z) of the function f(x,y,z) = 4xy + yz + 3xz at (1,1,1), (1,0,0), and…

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Q: Ix-yl 1 + |x-yl ₁ = R₁ d (x,y) = R is matric space

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Q: e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? +…

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Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: To find the extremum of f(x,y) subject to the given constraint. fx,y=2x2+4y2;        3x+4y=204

Q: f (x,y)=arcsin( x²+y² -1)+x² +y² -1 %3D aşağıdakilerden hangisidir? (ə) D(x,y)={(x.y)|1<x² +y² <2} 2…

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Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: We use langrange multiplier method

Q: 1. Consider the paraboloid f(r, v) = az + bry + cy", where we will assume that a, e 0. We will…

A: We have a given equation, f(x,y)=ax2+bxy+cy2 Then, D=4ac-b2 c) Without using the second derivative…

Q: Let D be the solid region bounded above by z = -3/x2 +y2 and below by z = -3. Then the projection of…

A: The region D is bounded above by z=-3x2+y2 and below by z=-3. So,

Q: Q: Evaluate the closed line integral p y³dx – x³dy C Where C is the closed path from point A(1,0) to…

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Q: 8. Evaluate the line integral (x'dx+ xe"dy where C is the closed path along the triangle in the…

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Q: Find the linearization of the function f(x, y, z) = xy+ yz + zx at the point (1,1,1).

A: Linearization of the function f(x,y,z) at (a, b, c) is given by…

Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

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