1. Let C be the closed loop that is traversed from (0,0) to (2,4) along the line y and then returns from (2,4) to (0,0) along the parabola y evaluate fo(ry + e3)dx – x²dy. Include a sketch and show all work. 2x %3D x2. Use Green's Theorem to |

Q: Use Green Theorem to evaluate C P xydx+e'dy where Cis the path from (0,0) to (1,1) along the graph…

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Q: Let P denote the path that travels along the graph of y = x2 from (0,0) to (1,1). Let f(x,y) = √1 +…

A: Let P denote the path that travels along with the graph of y=x2 from (0, 0) to (1, 1). Let f(x,…

Q: Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken…

A: Given that the integral,

Q: Evaluate the integra ∮C -y3 dy + x3 dx for any closed path C.

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Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: 42. Show that the graph of d ae""cos wi is bounded by y = ae-ct and y = -ae-ct for a > 0 and c> 0.

A: We know that,

Q: • Suppose that the mass in a mass-spring-dashpot system with m = 25, c = 10, and k = 226 is set in…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

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Q: Q2:- Evaluate / x + ydA where Ris the trapezoidal region with vertices given by R 5 5 (0,0), (5, 0).…

A: To find - Evaluate ∬Rx + y dA where R is the trapezoidal region with vertices given by…

Q: Find the absolute maxima and minima of the function on D, where D is the closed triangular region…

A: For finding the absolute maxima and minima values  Substitute the values of a vertices of a triangle…

Q: Find the SPI form of the Boolean expression whose Karnaugh map is below. yz _yz yZ ỹz 1 1 | 1 1 wx…

A: From the given table, the input value of Karnaugh map is…

Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x²…

A: (3)Let (x,y,z) lies on parabolaThe distance d=x-32+y2+z2such that z=x2+4y2Lagrabge multiplier…

Q: 3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) =…

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Q: 3. Use the method of Lagrange multipliers to find the minimum distance between the paraboloid z = x?…

A: Given,                               z=x2+4y2and the point (3, 0, 0).

Q: S :R\{0} → R, S(r)=e4z^+5z=2–1

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Q: (34) Compute SSp (6e3y + 1) dA where D is the solid triangle with vertices (0,0), (1,0), and (1,2).

A: Equation of the linejoining the points 0,0 and1,2  is  y-0x-0=2-01-0  Or,  yx=21=2  Or, y=2x…

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: 8. (a) Show that the system i=y+xf(r)/r, j=-x+yf(r)/r (7=x²+y?) (*) has limit cycles corresponding…

A: Given part (a) x·=y+xfrry·=−x+yfrrr2=x2+y2 By transforming coordinates into polar coordinates Thus…

Q: Consider the following semilinear first-order PDE ди ди +y ду = xe (i) Find the general solution to…

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Q: 2. Find the value of xy dx + Vy2 + 1dy, where C is the path shown on the graph below. (Hint: Use…

A: We have to find the value of  ∫Cxy dx + y2+1 dy. Given the path C is

Q: 2) Use Green's Theorem to compute f F. df where F=(3x +4y) i + 2xyj and C is the triangular path…

A: Use green's theorem

Q: 2) Use Green's Theorem to compute f F df where F=(3x + 4y)i + 2xyj and C is the triangular path from…

A:

Q: 17. Integrate f(x, y, z) = (x + y + z)/(x² + y² + z²) over the path r(t) = ti + tj + tk, 0 < a < t<…

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Q: 1)Prove that the curves o, = {|z|=2} y 0, = {|z- i|=4} are homotypic. 2)calculate O z*dz and o z*dz…

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Q: graph the points z = x + iy that satisfy the given conditions. 5. |z + 1| = 1 6. |z + i |= |z - 1|

A: Hi there, at a time we can answer only one question at a time and the exact one was not specified.…

Q: Use Green Theorem to evaluate $ xydx+e'dy where C is the path from (0,0) to (1,1) along the graph of…

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Q: (1. 1. 1) Evaluate the integral (5xy + 22°) dx + 5xf dy + (12z + 1) dz. (0.0.0) (Hint. Try the path…

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Q: 1. Compute SF · dr where F(x, y) = (y²,–x²) and C is the part of th parabola u = 12 from (-1 1) to…

A: First take dot product of f and dr Then put value of y in terms of x Integrate and raise limit of…

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

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Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

Q: Find the upper bound of e²²+1 zp- (z – 1)2 + 5“ where C is the circle |z – 1| = 2.

A: The integral ∫Cez2+1(z-1)2+5dzwhere C is|z-1|=2 To evaluate the upper bound of the integral

Q: 15. Evaluate the line integral J. (3x²y* - 6xy ]dx + (4x²y³ - 3x°) dv, where C is any path from…

A: My=Nx means F is conservative vector field

Q: Find the difference c-2d for the following cubic spline S(x) with natural boundary conditions: =…

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: (2) Let L be the line defined by 3 L(t) = 1 + and let p be the point (-1,6, 2). Find the minimal…

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Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

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Q: Let us consider the hyperbolic PDE is utt with the initial conditions c2U, 0 0 %3D u(x, 0) = P1(x)…

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Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: If A = 3.4xyâ + (1.7x² – 6.8y)âŷ, the circulation of A around the closed path shown below is

A: In this question, we have to find the circulation of vector A along the given closed field in fig.…

Q: Find the Wronskian of a given set {yı, y2} of solutions of 6. y"3(x21)y- 2y 0, given that W(T) = 0.

A: Given the differential equation and the value of the wronskian at pi as:

Q: 1. Use the Wronskian to show that the functions are linearly independent. Yı = e*, y2 = e2*, y3 =…

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

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Q: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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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: Let f(x, y)=V2x+4y² + 18-x. The domain of c for which the level curve f(x, y)=c is an ellipse is O…

A: Given function, fx,y=2x2+4y2+18-x To find the domain.

Q: Show that Si2 f dæ + g dy + h dz = S - (4xy³z*dx + 6y?x?z4dy + 8z°y³x²dz) is independent of path:…

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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).…