Define p: R^2 x R^2 to [0, infinity) by the rule p(x1,y1),(x2,y2)=squareroot((x1-x2)^2+(y1-y2)^2) Show that p is a metric on R^2.

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Q: Does the Divergence Theorem apply to surfaces that are not closed?

A: By Stokes' theorem:

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A: 2d graph of  x = z^2

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Q: Let y= - Find the intersection of these surfaces, Calculate the GB of wrt lex order x>4>2)

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Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…

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A: Function f(x, y) = -x2-y2 To Sketch the surface z=f(x, y).

Q: Integrate G(x, y, z) = y + z over the surface of the wedge in the first octant bounded by the…

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Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

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Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

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A: The general form of a parametrization of the circle of radius r parallel to yz-plane with center…

Q: Theorem; il f is entire ond bounded in the Camplex plane, then (2) Constant throughout the plane .·…

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A: We will assume S ⊂ R be a surface homeomorphic to a cylinder and with Gaussian curvature K &lt; 0.…

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A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

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A: Given that a conformal map that takes z | 0&lt;argz&lt;π8 onto the unit disk.

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A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

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A: Given that F=(x+y2)i-2xj+2yzk The divergence theorem is, ∭FdV=∭∇Fdxdydz On surface S1, y+2z=6,…

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A: Draw the region R as follows.

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A: Introduction: The orthogonal projection of a onto b line parallel to b is known as the vector…

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A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

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A: Given, surface σ is a plane x+y+z=1 that lies in the first octant. To find              ∬σ(2x+z)dS=…

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A: I have given the answer in the next step. Hope you understand that

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A: Given equation of cyrves, x=f(y)=y2-1,x=g(y)=1-y2

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A: Consider the given information. The formula for the double integral is defined as.…

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A: This is parameterisation of curve problem

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A: Plane.

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Q: Let X = R², x, y EX where x = (x₁, x2), y = (y₁.Y2) with the metric function (4 pts) (x, y) =…

A: This is a question of topology and metric space.

Q: Find the distance between the planes  5x − 3y + z = 5  and  5x − 3y + z = −9.

A: Two planes  and will always be parallel if The given planes  and  are parallel because we can see…