Evaluate R CF. dr with F(x, y, z)=(x2 + y)i – (3xz)j + (z – 4y) k, with the path C as the line segment that connects the point (1, 3, 2) to (2, 0, 0) and from (2, 0, 0) to (-2, 0, 0) along the semicircle y = V 4 - x2 on the xy-plane. %3D

Q: Evaluate Se (5xy + x² + y²) dx + (x² - y)dy by using Green's theorem, where C is a closed curve that…

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Q: (B) Prove that the stream line of b are counterclockwise circles, for that calculate F = Vx (-y ěx+…

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Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: Let C be the boundaries of x² + y² – 4y = 0 taken in the counterclockwise direction. A…

A: Let's find.

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…

Q: Find a piecewise smooth parametrization of the path C. (ti + tj 0 ≤t≤ 1 r(t) = 1 y 1 ≤t≤2 [y=√x (1,…

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Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

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Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, yo, 20) is given by the…

A: Given: Surface f(x, y, z)=c and a point x0, y0, z0 To show: Equation of tangent line to f(x, y, z)=c…

Q: 30. (2x + y²) dx + (2xy + 3y) dy C C: Any simple closed curve in the plane for which Green's Theo-…

A: We know that Green's theorem

Q: Find the maximum value of f(x, y) = 3ry(9 – 45x – 9y) over the triangle with vertices (0,0), (,0)…

A: Maximum value occurs at critical points or on the boundaries of the triangle.

Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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Q: Find a linearization L(x, y, z) of f(x, y, z) = x²y + 4z at (1,-1,2).

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Q: Find a parametrization a = #(t), y = y(t), t E [0, 1] for the line segment from (-2, –5) to (-3,…

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Q: Evaluate Vf dr where f(x, y, z) = 4xye and C is the path parameterized by r(t) = costi+ sin tj+tant…

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Q: dz (a) Use an appropriate form of the chain rule to find dx dz in terms of y in terms of x and if z…

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Q: Find a formulaforvectorfield F= M(x,y)i+ N(x,y)j given the fact that for all points(x,y),Fpoints…

A: Any point, x,y in the two dimensional space can be defined by a position vector, v→=xi+yj .

Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

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Q: Find the maximum value of f(x, y) = 9xy(5 – 25x – 5y) over the triangle with vertices (0,0), (, 0)…

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Q: find the linearization L(x, y) of the function ateach point. ƒ(x, y) = x3y4 at a. (1, 1), b. (0, 0)

A: Consider the function: fx,y=x3y4 To calculate the derivatives of the given function with respect to…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Integrate f(x,y,z) = x+ Vy -z° over the path from (0,0,0) to (3,9,3) given by C,: r(t) =t i+tj,…

A: The given function is, Let, Also the given paths are, So,

Q: Let C be the boundaries of x2 + y² - 4y 0 taken in the counterclockwise direction. A…

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Q: 2 The values of a and b such that the surfaces ax - byz = (a + 2)x and 4x2y + z3 = 4 cut…

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Q: Let F = (tan(3x) - y)i + (2x – sec-1y)j and C be the boundaries of the circle x2 + (y-4)2 = 9 in the…

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Q: Compute fS fdS for f(z,v, z) = 2y-z and S is the part of the cone 2-2+ betweenm z 1 and z 4.

A: Integration is the process of finding the anti-derivative function of a given function. The…

Q: 4. Prove that fer*dr+xydy = f, So*(y– 0)dydr where C is the triangular curve consisting of the line…

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Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

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

Q: f(x, y, z) = xe z2, piecewise linear path from (0, 0, 1) to (0, 2, 0) to (1, 1, 1)

A: To Determine: calculate ∫cxez2dx Given: we have piecewise linear path from (0, 0, 1) to (0, 2, 0) to…

Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? < 9, y 2 0. Then f.(-2ydx +…

A: A detailed solution is given below.

Q: Evaluate the line integral ∫CF⋅d r∫CF⋅d r where F=⟨4sinx,−cosy,xz⟩F=⟨4sin⁡x,−cos⁡y,xz⟩ and CC is the…

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Q: (b) Let z(r, y) = exp(-|r|) cos r + y², where r + y /9 = 1. Show that z(r, y) has minimum points…

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Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment…

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Q: Let C be the boundary curve counterclockwise of the semidisk x2 + y? < 9,y 2 0. Then f (-2ydx +…

A: Given Information -  C is the boundary curve counterclockwise of the semi disk x2 + y2 ≤ 9 , y ≥ 0…

Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: Evaluate § F · ds, where F = 2x(x+y)i + (x² + xy + y?)j and the positively-oriented curve C encloses…

A: Here we will use greens theorem to find line integral of vector field For a vector field F→= Pi^+Qj^…

Q: Suppose F(x, y) = (2 + 5y, 6z – 5y²). Use Green's Theorem to calculate the circulation of F around…

A: Given : vector field F→x, y=x2+5y, 6x-5y2 and triangle C oriented counter-clockwise with vertices…

Q: (b) Evaluate (3, 10) J(0, 1) Cto (3x + y) dx +(2y - x) dy along- @ curve y= x? +1; (ü) the line…

A: Given function is 3x+ydx+2y-xdy i) Given curve is y=x2+1 Hence the integrand becomes…

Q: Find the maximum value of f(x, y) = 3xy(11 – 132x – 11y) over the triangle with vertices (0,0), (,0)…

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Q: Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following…

A: To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are…

Q: Show that F(x, y, z) = (y² – e* sin z)i + (2xy + z)j + (y – e* cos z)k is conservative and hence…

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Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? 0. Then § (-2ydx + 3xdy) = a)…

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Q: Let C be the boundary curve counterclockwise of the semidisk æ? + y? 0. Then fc(-2ydx + 3xdy) 5dydx…

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Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? < 9,y 2 0. Then f(-2ydx + 3xdy)…

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Q: Sketch the plane curve. r(t) = 2ti-tj, [0, 2] y -1 y 2 1 Find its length over the given interval. 2…

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Q: *6. Let f: R' →R be given by =+4x'z-6xyz+4y-3x'y. Is M=f-((0}) a smooth surface (2-dimensional…

A: Given, fxyz=z2+4x3z-6xyz+4y3-3x2y2 Now, writing the given function in matrix form.…

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

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…

Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

A: a. Suppose,  F=∇fF=∂f∂x,∂f∂y So, ∂f∂x=12x+2+tan-1y∂f∂y=x1+y2+3y2 Now, ∂f∂x=12x+2+tan-1y Integrate…