Use Green's theorem to evaluate the line integral along the given positively oriented curve. yex dx + 2e* dy, C is the rectangle with vertices (0, 0), (5, 0), (5, 6), and (0, 6)

Q: PDE ut- 3leuxx 0LXLI も>6 B.C.: : ulo,t) = ULyt)=D0

A: In this question, we solve the wave equation by using the separation of variable,s and using given…

Q: Draw the contour curves for h (x, y) _y²+x² -1+2x and c = 0, 2, 4.

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

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Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

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Q: w=f(z)=z/(1-z) under transformation IzI=3 Find the image of the circle?

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Q: Show that t, e^t, and sin(t) are linearly independent.

A: In the given question we have to show that t, e^t, and sin(t) are linearly independent.

Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: Find div F and curl F if F(x, y, z) = xªi – 6j + yzk. div F= curl F=

A: To find  and  if .

Q: Find div F and curl F if F(x, y, z) = xzºi + 6y²x²j + 6z²yk. div F= curl F=

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