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

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

A: By Stokes' theorem:

Q: The Mobius surface is orientable. Select one: True False

A: A surface is orientable if it has two sides. Then, one can orient the surface by choosing one side…

Q: Find the surface area of the portion of the sphere x^2 + y^2 + z ^2 = 1 that lies abovethe cone z…

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Q: Let r < R. Revolving a circle of radius r, (x – R)² + y² = r², around the y-axis gives a donut…

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Q: Evaluate ff. xyz ds, over that part of a sphere of two units radius and centre at the origin Which…

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Q: Consider the area of the part of the plane z=ax+by+c that projects onto some region D in the…

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Q: 4. Show that the set of points (z, w) e C with w2 = sin z is naturally a Riemann surface. %3D

A: Let, S=z,w∈ℂ2|w2=sinz be the set in equation. The multivalued analytic function fz=sinz can be…

Q: Which of the following surfaces could have contour map 5 2 1 1. cone 2. parabolic cylinder 3.…

A: Please see the below picture for detailed solution.

Q: Consider the parullelepiped with Sider. t-Findthe Volume of the Paralletefiped 2 Findthe…

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Q: Surface at θ = 40⁰ and r = 20 is a     plane    cirlce   cone

A:

Q: 7. Which surface is parameterized by ř(u, v) = (u, uv, v) for –1 < u <1 and –1< v< 1?

A: r→(u, v) = u, uv, v for -1≤u≤1 and -1≤v≤1The parametric curve is  Option C is correct.

Q: Consider the portion of the plane x + 2y + 3z = 12 that sits above the circle (x − 2)^2 + (y − 2)^2…

A: The solution are next step

Q: Find vohume fome above ZVy-xLy, below Z0(xy plane) inside xy/ 3.

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Q: I, Use Stoke's theorem to evalueate S.Fidr, where F Cau2)= - it +x3 + 2î aind C is the Ceurve of…

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Q: Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and…

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Q: Verify Stoke's for F = (2x – y)i – yz²j – y²zk where S is the upper half of the sphere x? + y? +z² =…

A: Solution is given below

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = &lt;u,v,uv&gt; , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: Find the area of the portion, for which z > , of the sphere in R with radius v3 centered at the…

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Q: Show thata perojective plane of gives 0nder indeed BİBD (+n+l, n+),1)

A: We need to show that the projective plane of order n indeed gives a BIBD (n2+n+1,n+1,1)

Q: Let S be the surface parametrized by R (u, v) =< u, uv, uv

A: It is given that, the parametrized surface is R(u,v)=u, uv, uv2, 0≤u≤2, 0≤v≤3.  We have to calculate…

Q: Calculate both sides of Green's Theorem when F = [-x²y, xy²] and y positively oriented circle x2 +…

A: According to the given information it is required to calculate both sides of the Green’s theorem.…

Q: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: Show that the area of the plane region bounded by the curves,  x - y =7   and    x= 2y² - y + 3…

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Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

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Q: Evaluate the surface z =1,0<x,y <1.

A: To solve this we will use divergence theorem.

Q: Find a formula for the distance from the point P(x, y, z) to thea. xy-plane. b. yz-plane. c.…

A: Distance FormulaDistance between two points x1,y1,z1 and x2,y2,z2d=x2−x12+y2−y12+z2−z12

Q: What is the surface area of the portion of the surface z=x2+y that lays over the triangle on xy-…

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Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

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Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

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Q: Calculate ff A.n ds If A = yi + 2xj – zk and S is a 2x + y = 6 plane surface in the first octane cut…

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Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: Show the equivalence of the three definitions for the following 2-dimensional manifold: implicit…

A: Given: The given statement is shown as follows, implicit surface x2+y2=z2.

Q: Find the surface area of that part of the plane 8x + 9y + z = 8 that lies inside the elliptic…

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Q: Draw the parameterized surface. (Decide on a reasonable domain for u and v.)

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Q: An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and…

A: The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a…

Q: Show that the area of the plane region bounded by the curves,  x=y^2 -1,  x= 1 - y^2  is 8/3 square…

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

Q: Let C be a curve given by the intersection of the surfaces z = x2 +y2;z = 3−2x . The value of the…

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Q: classify the quadric surface given by equation and determine its standard form.−x 2 − y2 − z2 + 4x y…

A: Given quadric Surface is         -x2-y2-z2+4xy +4xz+4yz =3 Comparing it to the general form,…

Q: Find the surface area of a sphere of radius r

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Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: Classify the surface: 1- x = 3y2 + 422 O Ellipsoid O cone O Elliptic paraboloid O Plane sphere

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Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

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Q: 8. Let S be the part of the sphere r² + y² + z² = 2 where y 2 1, oriented away from the origin. (a)…

A: Given x2+y2+z2=2 where y≥1

Q: What is a flat surface that extends infinitely in all directions?

A: Plane.

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

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Q: What is the surface of the box formed by the net above

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Q: Show that the maximum value of abc on a sphere of radius r centered at the origin of a Cartesian…

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Q: Let y ==a and z =. Find the intersection of these х x2 surfaces.

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