b) Given F(x, y, z) = (x³ + cosh z) i+(2y³ – 3x²y) j – (x² + 4y²z) k. Use Gauss's theorem to calculate | F.n dS where n is the outward unit normal of o, the surface bounded by the planes, r = 0, z = 0 and x + z = 6, and the parabolic cylinder a = 4 – y². ITM

Q: Find the equation of the tangent plane (in the form z = ax + by +c where a, b, c are constants) to…

A: Here we use the formula of  ∂f∂x(a,b)(x-a)+∂f∂y(a,b)(y-b)=0 tangent plane to the surface at a point…

Q: ermine the point(s) on the surface z = 30x - 28y - 5x² - 7y² at which the tangent plane is parallel…

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Q: Let F= (0,0, z) and S be the part of the paraboloid z = x² + y² between the plan z = 1 and 2 = 4,…

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Q: Find the surface area of the portion of the part of the paraboloid z = 7 - 2x² – 2y² that lies above…

A:

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

A:

Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

A:

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: Find the regions of the (x, y)-plane where the equation (1+ x) + 2xy; Əxðy + 2y? 2 + x xy? + (1 –…

A: Given equation is, 1+x∂2u∂x2+2xy∂2u∂x∂y+2y2∂2u∂y2+x2∂u∂x-xy2∂u∂y+(1-y)u=0 The equation…

Q: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

A:

Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

A: S is the portion of the plane 2x+3y+z=2 lying between the points (-1, 1, 1), (2, 1,-5), (2, 3,-11)…

Q: The curve y = sin(πz), with 0 ≤ z ≤ 2, on the yz-plane is revolved once about the z-axis. Find a…

A: Given that y=sin πz and 0≤z≤2 The objective is to find the vector equation. The image formed is like…

Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

Q: b) Given F(.r, y. :) = (r + cosh 2)i+ (2y-3r*y)j-(r + 4y*:) k. Use Gauss's theorem to calculate F.n…

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Q: 03. a. If F = (y² + z² − x²)i + (z² + x² − y²)j + (x² + y² − z²)k, then evaluate, SSV × F·n dA…

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Q: Consider the ellipsoid 4x2 + 2y2 + z² = 27. Find all the points where the tangent plane to is…

A: We have to find the points.

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: Find the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

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Q: b) Given F(r. y. :) = (r* + cosh : )i+(2y – 3.r"y) j - (r + 4y:) k. Use Gauss's theorem to calculate…

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Q: x² - y²-2²-4x - 2z+3=0

A: The given surface is x2-y2-z2-4x-2z+3=0T is the trace of S using x=2.To find the two cordinate when…

Q: • SS,F. F = (4x³z, 4y³z, 3z¹) Calculate F.ds where and S is the surface of the solid bounded by the…

A: Given,                           F→=4x3z, 4y3z, 3z4, and S is the surface of the solid bounded by…

Q: Find the equation of the tangent plane at the point - 2 of the surface * = 0 3, y = yo z = f(x, y) =…

A:

Q: Let S be the quadratic surface given by S = {(x, y, z) | z = 4x² - y², z ≥ 0}, oriented with the…

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Q: Evaluate ff F.n ds where F(x, y, z) = 12xi +24j+24x²k and is that portion of the paraboloid z = x² +…

A: We will find normal vector n and region of integral on xy plane to find value of integral .

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.