Evaluate the integral |(2e' – 2x) dy +(2xy +1) dx using Green's theorem where C is C 64 ans:-- 3 consists of y = 4-x and straight line from (-2,0) to (2,0). Sketch the curve C.

Q: Evaluate [F·dr if F(x, y)=(4e³)ī +(4xe³)j and the curve C' is line segments going from (0,0) to…

A: To evaluate ∫C F⇀·dr⇀ if F⇀x, y=4eyi⇀+4xeyj⇀ and the curve C is line segments from 0, 0 to 5, 4 to…

Q: Find div F and curl F if F(x, y, z) = 16yªz³i – 17x7zºj − 3xy¹k. div F= curl F=

A: Given: F(x,y,z)=16y4z5i-17x7z6j-3xy7k. To be find: div F∇.F and curl F∇×F. Concept: for a vector…

Q: Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

A: The plot of the curve for t within 0 to 2pi is shown in figure below.

Q: Q2] Find the analytic function F(z) if u = coshy.cosx, (B.C. v-0 at x=0)

A: at

Q: Let y = f(x) be defined parametrically as y=t+tt, x = 2t -t, te R. Find f(x) and discuss its…

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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: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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Q: In(t + 4) sin2t Given the vector valued function 7(t) = (e-3t, t a) Find the domain of 7(t). b) Find…

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Q: Let C be the curve consisting of line segments from (0, 0) to (1, 1) to (0, 1) and back to (0, 0).…

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Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: Consider f (x, y) 3x² + xy + 3y². Use calculus to find the extreme values of fon the circle x² + y²…

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Q: (a) Use a Green theorem to evaluate (y¹ - 2y)dx - (6x - 4xy³). dy where c is the boundary of the…

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Q: ôw ôw + = 0 for w = Ax, y), x = u – v, and y = v – u and demonstrate the ди ду 6. Show that result…

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Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: Consider the function f(r, y) = 212 + ry – 6ry + 5x +2. (a) Show that (1,3) is a stationary point of…

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Q: Find the equation of the tangent plane to the surface z = cos(6x) cos(3y) at the point (-2π/2,…

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Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Construct an analytic function of the form f (z) = u + iv, where v is tan- (y/x), x # 0, y # 0

A: f(z)=u+iv where v=tan-1(yx)  We need to find the analytic function f(z)=u+iv  we apply Milne Thomson…

Q: Let F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F - (b) What…

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