Find the area of the following surface using a parametric description of the surface. The plane z= 18 -x- 3y above the square |x| s 4, ly|s4 The area is (Type an exact answer, using radicals as needed.)

Q: z =x' +y° +1 Y L x' +y? -z? = 1 LY

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Q: Consider the surface S which is the part of the paraboloid y = x ^2 + z^ 2 that lies inside the…

A: Given, the surface S: y=x2+z2 which lies inside the cylinder x2+z2=16.   a) Let x=vcosuz=vsinuThen…

Q: Verify that the curve r(t) lies on the surface. Give the name of the surface. r(t) = (/3t cos t, V3t…

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Q: b) The curve y = }(r² – 2 In r), 1<r< 4, is rotated about the y-axis. Find the area of the resulting…

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Q: A parametric representation of the surface y? + z² – x² = 0 in R³ is given by, Select one: O a. æ =…

A: option (b) is correct.

Q: Consider the surface S given by the equation e^(yz) + z(e^z) + x^2 z^2 = 2e. (a) Check that the…

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Q: Find all points on the surface given below where the tangent plane is horizontal. 2 Z=X ? - 3xy-y -…

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Q: Evaluate the surface integral below where S is the cone with given parametric equations xzds ,wher S…

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Q: The trace of the surface S: z =a + y? in the plane z= 4 is O a Line O a Parabola O An ellipse O a…

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Q: x² + y? that is below the plane Find the surface area of that portion of the paraboloid z = z = 2.

A: Given paraboloid z=x2+y2 Surface area, AS=∫∫R∂z∂x2+∂z∂y2+1dA AS=∫∫R2x2+2y2+1dA…

Q: For the surface with parametric equations r(s, t) = (st, s + t, s - t), find the equation of the…

A: Use equation of tangent plane

Q: 3. Consider the curve y = x°, 0<x < 3. (a) Find parametric equations for the surface obtained by…

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Q: Find the area of the surface cut from the paraboloid x² + y² -z = 0 by the plane z = 6. The surface…

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Q: Identify the surface defined by the following equation. 2x-y +z? = 0 The surface defined by the…

A: Form of equation               Surfacex=Az2+By2                     Eliptic Praboloidx=Ay2-Bz2…

Q: for the Surface Area below ... what is the * ?radius of revolution The area of the surface obtained…

A: The radius of the revolution is the distance between the centroid of the curve and the axis of the…

Q: Given the cone z = x + y and the plane y + z = 1. (a) Parametrize the intersection of the cone and…

A: Here is the solution of the given problem.

Q: Consider the surface defined by the equation 2.x2 – 2y2 – z = 0. (a) Choose any one of the variables…

A: The equation is the form z=f(x,y) represents a surface in the space. In this problem the equation of…

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: Let S be the surface of the portion of the cone z? = x² + y² that is contained in the cylinder r? +…

A: According to the given information, let S be the surface of the portion of the cone that is…

Q: Consider a surface S, which is described by z=−6⋅y−6⋅x+12, with x≥0, y≥0. a) The area of surface S…

A: We will find out the required solution.

Q: For each of the following cases in cylindrical coordinates, explain the types of surface you get.…

A: a) When z is constant, the obtained surface will be a plane parallel to x,y,0

Q: Find a parametric representation for the surface. The part of the sphere x2 + y2 + z2 = 16 that lies…

A: Given:   Equation of cone z=x2+y2   Equation of paraboloid z=x2+y2  Imagine a sphere of radius…

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: The quadric surfaces 16x + 16y = 1 and 4z = x² – y? intersect in a curve. Parametrize this curve.…

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Q: Consider the surface 4a? – y? + 2z² + 4 = 0. a. Find the value(s) of k such that the cross-section…

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Q: Consider the plane curve C ∶ r(t)=(1/3t^3, 1/2t^2) (a)Make a table of values and sketch the curve…

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

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Q: • What is/are the trace(s) of the surface (x – 1)? 22 = 1 on the rz-plane? 36 a. hyperbola b.…

A: For the given surface

Q: The area of parametric surface S which is given by r(u, v) = (u+ v) i+ (u- v)j+ (u+v) k; 0<u< 1,…

A: The solution for the asked question is given as

Q: The ancient Japanese hand fan pictured below is described parametrically by *(u, v) = (v² cos(u), v²…

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Q: Given the surface z2 = x? – y² and the plane x – y= 1. (a) Parametrize the intersection of the…

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Q: Find the surface in the accompanying area of the heli r(r,0) = (rcos0)i+(r sin 0) j + Ok, 0s0<2r,…

A: Introduction: The formula for the surface area of the function r(r,θ) is given by,…

Q: Find the area of the following surface using a parametric description of the surface. The plane z =…

A: z=18-3x-3y x≤2,y≤2

Q: O Find the area of the auface, using Polar oordinates, of the portion of the Cone x²+y² - 9z²=0…

A: Use polar coordinates x=rcos(theta) y=rsin(theta)

Q: Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the…

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Q: The parametric form of normal line to the surface z = 2x² +y? at (1, 1, 3) Ox =1- 4t y = 1- 2t z…

A: First option is the correct option. Find the function f (x, y, z) from the equation for the surface.

Q: Find the area of the surface. The surface with parametric equations x = u?, y = uv, z =v?, o sus 2,…

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Q: Find a parametric representation for the surface. the part of the plane  z = x + 2  that lies inside…

A: We need to find parametric representation.

Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: What is the area, br^2, of the surface of the revolution obtained by rotating the graph of the…

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Q: 7. Consider the parametric surface S given by r(u, v) = 3u cos vi+ 3u sin vj + u? k, for 0 <u < 2,…

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Q: Find the area of the surface cut from the paraboloid x? + y +z=0 by the plane z= - 20. The surface…

A: The given equation of paraboloid is: x2+y2+z=0

Q: Using polar coordinates, evaluate J*** dydr, R where R is the semicircular region bounded by the…

A: For a function f(x, y) In Polar coordinates x = r cos θ, y=r sin θ Find f(r, θ) Formula Used: ∫∫R…

Q: Find a parametric representation for the surface. the part of the sphere x2 + y? + z? = 16 that lies…

A: The solution is below.

Q: For the parametric surface r(u, v) = (u cos v, u sin v, 0) where 0 ≤ ≤2 and 0 ≤ ≤ 27 and which is…

A: Given r(u,v)=u cosv, u sinv, 0 where 0≤u≤2,  0≤v≤2π r→u=cosv, sinv, 0 r→v=-u sinv, u cosv, 0…

Q: $ Find. the equation.f.the. tangent.plan. bo.the given.surface.at.thespeei fied.praint..…

A: The equation of tangent plane to the surface  F(x,y,z)  at the point (a,b,c)is given by…

Q: Find the area of the following surface using a parametric description of the surface. The plane z =…

A: In this question, concept of area using integration is applied. Integration Integration is a method…

Q: consider the straight y = λεR r : „z= 0 The surface S, obtained by the revolution of r around the y…

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