α : ℝ -> ℝ3   ,  α(t) = (t2+1 , 0 , t) is a curve. Let M be the surface obtained by rotating the curve around the x-axis.  1) Prove it M is a surface. 2) Find a ϕ(U) simple surface such that contains ϕ(1, π/4)  in M. Note: This is differantial geometry problem. Thank you in advance.

Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

A: a. this equation is in form of  as sign of A and B is opposite it is  Hyperbolic paraboloid

Q: Assume S is the surface x1000+y8000+z1000 = 10¹2 and f = (9+ eyz, x³yz, 3x - 5y - 6 cos(zx)).…

A: Here we use the Divergence theorem for a surface S inclosing a volume V

Q: sider the surface z = f(z, y)=√√/25 - 1² - y².

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Q: 2. Consider the surface defined by 1² + 2xy + y² + 2²-25 Let F(x, y, z)-1² + 2xy + y² + 2². (a)…

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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: Let E be the surface with equation (y – 4/2)2 1. | 32 52 42 (a) Give equations of the traces of E in…

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Q: Consider the surface z = (x + 1)² + (y – 2)² – 1 - Select an equation of the tangent plane to the…

A: we have to find the equation of the tangent plane of the surface 2=(x+1)2+(y-2)2-1 atthe point…

Q: 1. For 3x - 5y? – 10z? = -30 (a) Identify the type and describe the quadric surface. (b) Calculate…

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Q: Given z=12+73x² is a curve in the xz-plane. If the equation of the surface generated by revolving…

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Q: Let E be the surface with equation (y – 4/2)2 1. | 32 52 42 (a) Give equations of the traces of E in…

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Q: 6. Sketch the surface x² - + 4 4 (a) What are the traces of this surface in the plane x = C (where C…

A: The equation of the given surface is  .(a) To find the traces of this surface in the plane .(b) To…

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: (4) Sketch the surfaces. Show some work including intercepts. (a) z² + 2? = 4 (d) + y² + z² = 1 (b)…

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

Q: 4. Let f(x, y) = V2x² – 3y². (a) What is the domain of this surface? (b) Draw three level curves of…

A: This is a problem of analysis of several variables. Contour and trace a graph.

Q: Name the surface and draw an accurate Graph of x² – y² – z² = 1 in R’.

A: Given: The surface x 2 - y 2 - z 2 = 1     To determine: The name of the given surface and the graph…

Q: 2. -) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the…

A: Let's find equation of tangent plane and parametric equations of normal line.

Q: Let E be the surface with equation (y – 4/2)2 1. | 32 52 42 (a) Give equations of the traces of E in…

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Q: (P) is a circular paraboloid around z-axis and (Q) is the surface given by + += 1 This option (P) is…

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Q: Consider the following surface: z = x2 - (y2 / 4).  By hand, without any graphical utilities, find…

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Q: (a)) The base point of the surface is (0,0,0) and its axis (of symmetry) is the line (x, y, z) = (0,…

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Q: Find parametric equations for the surface obtained by rotating the curve y = eX, 0 sx 5 4, about the…

A: Consider the curve y=e-x,    0≤x≤4 Recollect: The parametric equations of the surface obtained by…

Q: 13. Consider the surface x² − 3y² - 9z² = 0. Which of the following is/are correct? (A) The traces…

A: Given: A surface x2-3y2-9z2=0, To Find : Which of the following is correct? a) The traces in the…

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: Prove that v5 is irrational.

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Q: Given surface A: 4x² − 9y² = 9(z² + 4) 1. Identify the type of quadric surface for A. 2. Give an…

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Q: Find all points on the curve e = {{r,y) : x² – ry + y? = 7} where the tangent line to C is…

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Q: Find the traces of the given surface in the planes x = k, y = k, z = k. Then identify the surface…

A: Given the surfaces, we need to find the traces on the planes x=k,y=k,z=k.(a)Consider the surface…

Q: Let (P) be the surface given by the following equation + 4 and (Q) be a surface given by the below…

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Q: Consider the intersection of the surfaces x² + y² = 1 and x + 2y + z = 0. (a) Sketch the surfaces…

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Q: The following equation is an equation of a surface of revolution obtained by rotating a curve C…

A: The given equation of surface of revolution is x2+y2+z2=1. This equation can be written as:…