4y - y² traced from (0, 4) to (0,0) while 1. Let C = C₁UC2, where C₁ is the semicircle x = C₂ is the line segment from (0,0) to (0,4). a. Use a line integral to find the area of the surface b. Use Green's Theorem to evaluate S := {(x, y, z) € R³ : (x, y) € C₁, 0 ≤ x ≤ x²}. e fryd xy dx - x² dy.

Q: find the tangent plane to the surface z = Vy-x at the point (1,2,1)

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A: The given surface is:ϕ(u, v)=u2+v, u, v

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A:

Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

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Q: (x² + xy) dx + (y² - xy) dy; C: the line y = x from the origin to the point (2, 2).

A:

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Q: H. Use the gradient to find the equation of the tangent plane to each of the surfaces at the given…

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A:

Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

A:

Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

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Q: Use Green's theorem to evaluate the line integral r ry dr+r² where C is positively oriented curve…

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: line integral x³ dy), where y is t 3 X counter clockwise.

A:

Q: Given: Find (a) div F (b) curl F

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Q: Let C be the positively oriented square with vertices (0, 0), (2,0). (2, 2). (0, 2). Use Green's…

A: Green's Theorem:  For a positively oriented curve C∫CP dx+Q dy=∫∫D∂Q∂x-∂P∂y dAfor the region D…

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Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

A:

Q: Let f(x,y)=/4– 4x² – y² . Find its domain and give a rough sketch of its surface.

A: The given function is:fx, y=4-4x2-y2To find domain and sketch the surface

Q: 3. Find integral surface of the equation x³p+y(3x² + y)q = z(2x² + y) which passes through the curve…

A: