Let M⊂R ^ 3 be a surface and f be a diff.bilir function on this surface. Show that if Q is this surface M a 1-form on then d(fQ) = df∧Q + fd

Q: Describe and sketch the surface (x2/16) - (y2/9) + z2 = -1

A: The given surface x216-y29+z2=-1. We have to sketch the graph of the surface.

Q: Does the Divergence Theorem apply to surfaces that are not closed?

A: By Stokes' theorem:

Q: For a given surface z-x^2-y^2=10 Find the parametric representation of the straight line which…

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Q: 32²+62-4x-3y+2=0. 1. identify the surface: Present a well-defined sketch of the surface.

A: Given, the surface               2x2-3z2+6z-4x-3y+2=0

Q: Sketch or describe the surfaces in R³ of the equation presented x² + y} – 2x = 0

A: The equation is x2+y2-2x=0

Q: Identify the type of quadric surface defined by the equation and find all x-, y-, and z-intercepts…

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Q: Consider the Folowing equation of a quadric surface 4×^2+9y^2+9z^2=36 a. Find the intercepts with…

A: Given question is Consider the following equation of a quadratic surface4×^2+9y^2+9z^2=36. We have…

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: A surface is defined by coordinate or parametric functions of more than two variables. Select one:…

A: A surface is defined by coordinate or parametric functions of more than two variables.

Q: calculate ∫Cy(x-z) ds, where C is the intersection of the surfaces x2+y2+z2=9 x+z=3

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Q: Use LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2,…

A: Given surface z2=x2+y2 and the point (4,2,0). The objective is to find the points on the surface…

Q: Explained every step

A: The given equation of the surface is  x2 + 2y2 + z2 − 4x + 4y − 2z + 3 = 0.   The general equation…

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

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Q: Sketch and identify the surface given by x2 + 4y + 4z2 = 0.

A: Equation of the surface is given by:x2+4y+4z2=0 we need to identity the surface and hence sketch the…

Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: Sketch the surface given by the equation x2+z2/3+y=3 indicating the points where the surface…

A: Sketch the surface given by the equation x2+z2/3+y=3   indicating the points where the   surface…

Q: find the points on the surface

A: Given, S: x2-y2+6z=0=fx,y,z where normal line to the surface is parallel to the line passing through…

Q: Let S be the quadric with equation 36x² –4y² –9z² – 36x = 0. Sketch a graph of the surface with…

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Q: Describe the surface whose equation is given by x² + y² + z² + 6y - 2z = 0.

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Q: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain

Q: d(fv) = df ^ ¢v + fdý %3D

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Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

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