Work Problem Let C be the portion of y = x2 - 2 from x = -3 to x 3. a) Sketch the curve C. b) For the given curve C, evaluate the line integral F. dr, where F(x, y) = x² yi + (2x + 3y)j.

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A: Solve the integral by substituting the curve in the question.

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Q: e Green's Theorem to evaluate [(-y²)dx + (x²)dy if the curve C is a triangle with rtices at (0,0),…

A: Top:- application of integration

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A: Hello. Since your question has multiple parts, we will solve the first parts for you. If you want…

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Q: etermine the equation of the plane tangent to the surface x2 + y² – z² = –1 at the point , 1, v3).

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Q: Use Green's Theorem to evaluate fa F. dr where F(x, y) = (y cos x, x² + 2y sin x) and C is the…

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Q: Find equations of the tangent plane and normal line to the surface z +1 = xe" cos z at the point (1,…

A: Solution:- z+1=xeycos z at the point 1,0,0 take function as; fx,y,z=z+1-xeycos z ∂∂xf=fx=-eycos z…

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Q: 9. Find an equation of the tangent plane to the given surface z x sin(x + y) at (-1,1,0).

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Q: The differential of plane curves described. 1. the cissoids y^2 = x^3 / (a-x)

A: y^2 = x^3 / (a-x)

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A: We can calculate by integrating.

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Q: Consider the family of curves y I 1+ GI

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Q: equation of the tangent plane to a surface z = f(x, y) = ln ( /4x² + 9y² + 2x at the point P(-2,1).

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 10. Curve tangent to a surface Show that the curve 4 (G-) ( - 3 j + cos (t – 2)k r(t) = 2 i + is…

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Q: 9. Find equations of tangent plane and normal line of surface e -z+ xy 3at point(2,1,0). %3D

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A: We will find out the required parametric equation.

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Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (1,2,0) on the…

A: Let,  ϕ=-8cosπx+3x2y+exz+5yz-15∇ϕ=i∂ϕ∂x+j∂ϕ∂y+k∂ϕ∂z…