(b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz, where the curve C is the intersection of the paraboloid z = x2+y? – 1 with the plane x + y – z = 1, oriented counterclockwise viewed from above.

Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: a) Consider the surface z = Find the tangent plane to the 3. surface at the point (4, 3, 5). (4.04)3…

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Q: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

Q: The equation of the tangent plane to the surface 32 = x² + y² +1 at (-1,1,2) is O A.-2x-2y+3z = 2 O…

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Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

Q: Find the points on the surface 2a2 + ly² + 522 = 1 at which the tangent plane is parallel to the…

A: We will use the following method for finding the two required point.

Q: Calculate dz – yz dy – sen(2)dz, where Cis the path connecting the point A(-2, 2, 4) to the point…

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Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

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Q: f (yx − xỹ + z2) · ds around the circumference of the circle with radius 2, center at the origin, in…

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Q: a) Use Green's theorem to compute f F dr where c is a circle of radius R oriented CCW and F(x, y) =…

A: Green's theorem:∫C[Pdx+Qdy]=∫∫T∂Q∂x-∂P∂ydxdy where T is the region bounded by a simple closed curve…

Q: Let F(x, y) = (3+2xy²) i+2x²yj. Find a function f such that F = Vƒ and use it to evaluate F. dr…

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Q: i) Calculate length of the curve r(t) = acost î+ asint ĵ+ 4t k from (a,0,0) to (a,0,87).

A: As per our company guideline we are supposed to answer only one question kindly post remaining…

Q: Consider the surface S parametrized by Þ(u, v) = (u², v², √√2uv) where 0 ≤ u ≤ 2 and 0 ≤ v ≤ 2.…

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Q: Show that the graph of the parametric equations x = a + (c − a)t, y = b+(d−b)t, t ∈ [0, 1] is a line…

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Q: Encik Samsudin, a PhD student has reported the concentration of E.coli bacteria, C(μg/L) in a…

A: Given: C=kmaxt25+2t2+3.5t To find the root and to determine the fastest time for the E.coli…

Q: Find a parametric representation for the surface S, where S is the part of the cylinder x2+y2 = 4…

A: A surface S where S is the part of cylinder x2+y2=4 which lies between z=-2 and y+z=2. To Find:…

Q: prove hat for 4 x² + y² + z² + 6xyz + 2x² - y² +z²+ 4yz + 3zx = 0, rigin is a conic node. the locus…

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Q: If V=R\power{3}, and W\index{1} is the xy plane and  let W\index{2} is yz-plane:…

A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…