[(cos y + 3xy²)dx +(4x²y-xsin y)dy Use Green's Theorem to evaluate the line integral (0,0) to (0,1) (0,1) to (2,1) to (0,0) where C' is the triangle from

Q: 5. Find an equation plane to the surface (u, v) = (3 cos(u) sin(v), 2 sin(u) sin(v), cos(u)) at the…

A: First, we find the point on the surface where the tangent plane would be drawn. Next, we calculate…

Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: F(x, y) = (4x³,3y²) along a path from (0, 0) to (2, 6). Find S F · dř. a) using a parabolic path. b)…

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Q: Use Stokes' Theorem to compute 1 z? dx + (ry) dy + 2020 dz, where C is the triangle with vertices at…

A: Given I=∮C12x2+xydy+2020dz where C is the triangle with vertices at 1,0,0 , 0,2,0 , 0,0,2 traversed…

Q: Qz/ Evaluate the complex integral: dz (z+ 1)(z – 2) where C is: a) The circle Iz] = 3 b) The circle…

A: Note:- If z =(x+i y)  then z =x2+y2 Cauchy's Residue Theorem:- ∮Cfz dz =2πi sum of residue   Given…

Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

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: Evaluate F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

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Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: CD has coordinates C(-8,-2) and D(-4,-12). determine the coordiantes of C'D' if (x,y) -> (1/2x,1/2y)…

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Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: √4-x² So fo 0 [ r x² + y² dy dx

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Q: Although this integral could be written as 3 9-z2 (9 - x2 - z2) vx² + z²dz dx it's easier to convert…

A: Given  ∫-33∫-9-x29-x2(9-x2-z2)x2+z2dzdx

Q: Let C be the curve connecting (0,0,

A: Given that C be the curve connecting  (0, 0, 0) to (1, 4, 1) to (3, 6, 2) to (2, 2, 1) to (0, 0, 0).…

Q: 16. Sketch the cycloid r(t) = (t- sint, 1 - cos t) together with its tangent vectors at t = and .…

A: Solved the above problem.

Q: Encuentre TLt), NCt) B (t) de cLE) = ( cost , sent, t)

A: We will use the respective definitions.