Consider the surface: S:z = 4 – a?, in the first octant and bounded by x² +y°, as shown in the following figure. as shown in the following figure.

Q: Evaluate the surface integral F. dS where F = (4x, -5z, 5y) and S is the part of the sphere x² + y +…

A: The solution is given below:

Q: Use Green's theorem to find the surface integral of the following geometry if V = xy'i - x³yi, and…

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Q: Under what conditions can you find the area of the surface generated by revolving a curve x = ƒ(t),…

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Q: (c) The cone r² = 4(y² + z?) for (0 <x < 4

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Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

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Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

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Q: Let S be the part of the hyperbolic paraboloid z = x2- y2 located between the cylinders x2 + y? = 1…

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Q: Evaluate the surface integral 2 = 1 which is in the first octant. ry dS, where S is the part of r+y+

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Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

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Q: Evaluate the surface integral| f(x.y.z) dS using an explicit representation of the surface. f(x.y.z)…

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Q: Evaluate the surface integral. ∫∫sxdS, S is the part of the plane 6x+3y+z=6 that lies in the first…

A: The plane has intercepts at (1,0,0), (0,2,0), (0,0,6). The parameterize the surface S by. where

Q: Let Sj be the closed surface consisting of S in Figure with the unit disk. Find the volume enclosed…

A: Given: S1 is enclosed surface of S

Q: Given a surface 3xy - In (4z – 3) = 0, where z = decimal places. f(x,y). Find zx at y = -6, z = 1.…

A: We have given  3xy - ln(4z - 3) = 0             3xy= ln(4z-3)             4z-3= e3xy…

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Consider the oriented surface S for z > 0, consisting of the portion of the surface of the…

A: To sketch the given surface.

Q: Evaluate the surface integral. 2,2 ds S is the part of the cone + y that lies between the planes z =…

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Q: Evaluate the surface integral: x dS,  S is the part of the plane  12x + 6y + z = 12  that lies in…

A: From the given statement, the plane is 12x + 6y + z = 12 and it is lies in the first octant.

Q: Evaluate the surface integral. y² ds, S is the part of the sphere x² + y² + z² = 1 that lies above…

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Q: Use Stokes' Theorem to evaluate | F - dr, where F (x, y, z) = zi + yj – xk and C is the 9 – z? y? in…

A: Given F→x,y,z=zi^+yj^−xk^ We have to evaluate ∫CF→⋅dr→,where C is the boundary of the part of the…

Q: Find the area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Consider the surface S={(x, y, z)| xy+ z= 5; x20; y20; z20} in R3. Use the Method of Lagrange to…

A: The distance between points can be calculated using the distance formula. The distance formula is…

Q: Find the area of the following surface using a parametric description of the surface.   The cap of…

A: Consider the surface that is the cap of sphere:

Q: If the infinite curve  y = e−4x, x ≥ 0,  is rotated about the x-axis, find the area of the…

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Q: If the curve y = f(x), a ≤ x ≤ b, is rotated about the horizontal line y = c, where f(x) ≤ c, find a…

A: Given, Curve y= f(x) , a≤x≤b Rotated about a horizontal line y=cwheref(x)≤c

Q: Given a surface 2xy - In (3z- 2) = 10, wherez=f(x, y). Find zx at y =7, z= 1. Leave your answer…

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Q: Under what conditions can you find the area of the surface generatedby revolving a curve x = ƒ(t), y…

A: Given information,x=fty=gt; a≤t≤b To get the area of the surface generated by the curve about…

Q: #3. Evaluate the surface integral xz ds, where S is the part of the plane 2x +2y +z = 4 that lies in…

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Q: Given a surface 2xy - In (5z - 2) = -10, where z = f(x,y). Find Zx at y = -10, z = 1. Leave your…

A: Partial differentiation

Q: 4. For r > 0 and h > 0, show that the conical set S = (x, y, z) | x > 0, y > 0, z > 0, z2 h?(r2 - x²…

A: Given that the surface S is S=x,y,z|x&gt;0,y&gt;0,z&gt;0, h2=h2r2-x2-y2 We have to find the surface…

Q: Find the area of the surface generated by revolving about the y-axis the arc C given by C = { (x,y)…

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Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains point…

A: Given function is, z=lnx2+y2

Q: Let S be the surface given by the first octant part of the paraboloid z=4-x^2-y^2. Find the area of…

A: We need to determine the surface area of the surface bounded by the paraboloid: z=4-x2-y2 in the…

Q: Evaluate the surface integral. z2 ds, S is the part of the paraboloid x = y2 + z? given by 0 < x < 1

A: Evaluate the surface integral.

Q: Given a surface 3xy - In (3z - 2) = -5, where z = f(x,y). Find zx at y = 3, z = 1. Leave your answer…

A: This question is based on Partial differentiation of function

Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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Q: Find the area of the surface that is generated by revolving the portion of the curve yx' between x0…

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Q: Evaluate the surface integral fF- dS where F = (52,-52, 5y) and S is the part of the sphere a² +2+22…

A: Solution

Q: S y = 3 – 2 4z – 4 = 3(x +1)?

A: Let us start solving the problem step by step

Q: Which of the following is the surface area of the surface generated by revolving the curve y = in…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The spherical surface S is tangent to the z=0 and x+y+3z−2=0 planes, with (−1,2,0) being one of the…

A: Explained below

Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: Find, by using polar coordinates in R2, the volume of the region bounded by the paraboloid z = 20 –…

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Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

A: The function of the curve is y = 6x(x-1)2.

Q: Evaluate the surface integral. SS, xz ds, S is the part of the plane 2x + 2y + z = 4 which is in the…

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Q: Determine the sections of the following surface on planes parallel to the xz plane. -y+ = 1 %3D O…

A: here first we solve for the surface and then check it .

Q: Evaluate the surface integral. (x²z. y?z) as x2z + S is the hemisphere x2 + y2 + z² = 4, z 2 0

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Q: Find the exact area of the surface obtained x=t°, y =t 0<t<lby rotating about the x- аxis.

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