Evaluate the integral ff ds, where f(x, y) = y cos(2x) and C is the triangle with vertices at the (0,1), (1,0), and the origin.

Q: Use Green's theorem to calculate §. -y² dx + xy dy where C is the vertex triangle (1,3), (4,0) and…

A: Consider the given integral. I=∮c-y2dx+xydy The green theorem is defined as, ∮cPdx+Qdy=∬R∂Q∂y−∂P∂x…

Q: Suppose that the temperature T at point (x, y, z) is given by T(x, y, z) = sin(xyz) and that an…

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Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: Find three different parametrizations of the graph of y = x3.

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Q: Find the Jacobian for the change of variables defined by x = r cos θ and y = r sin θ.

A: To calculate the Jacobian for the change of variables, we need to calculate the following…

Q: (b). Use Green's Theorem to evaluate SF. dr. F(x, y) = (e³x², 2xy), where C is the triangle from…

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Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please…

A: [x,y]=meshgrid(0:2*pi); z=sin(x)+cos(y); surf(x,y,z)

Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: Find Fouricr trmsform of uft-1)

A: Given problem is related with Fourier transform . Given that,                  xt = e-2t-1 ut-1 . We…

Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: d the polar coordinates if (x, y) = (-√3, 1), r≥ 0, -2π < E

A: Given query is to find the polar coordinates.

Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…

Q: particle started at A(1,0) circled the origin once  an d returned toA(1,0) .what were the change in…

A: Given: A particle started at A(1,0) circled the origin once  and  returns to A(1,0)

Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: Let w = iz2-4z+3i. find (a) Δw, (b) dw, (c) Δw-dw at the point z=2i

A: Consider the provided question, (a)

Q: Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.

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Q: Evaluate F dr where C is the line segment from (7,-,1) to (20, 1, and F (sin(yz) + 1)i + (zz cos(yz)…

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