2. Let F = xi+yj + zk and let f(x, y, z) = x² e²-². (a) Describe a surface S together with orientation so that (b) Explain why you cannot find a surface S so that Issi S F. d5 <0. √ [ f(x, y, z)ds < 0.

Q: Show that the curve r= Vti + Vtj + (2t – 1)k is tangent to the surface x +y² – z = 1 when t=1

A: Given that r=ti+tj+2t-1k and f=x2+y2-z-1 Take the derivative for f, ∇f=ddx,ddy,ddzf=2x,2y,-1…

Q: Let z = g(x, y) = f(3 cos(xy), y + e™v) provided that f(3, 5) = 5, f1(3, 5) = 2, f2(3, 5) = 5. i)…

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Q: Given the surface 2x² + y² = 3+z², (a) find the points on the surface where the tangent plane is…

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Q: Find the tangent planes to the surfaces given by the equations z = 7x^2 - 12x - 5y^2 and xyz^2 = 2…

A: NOTE: Refresh your page if you can't see any equations. . the first surface is so we can write…

Q: Suppose that an equation for the surface is S(x,y) = xye^x. In what direction (relative to the…

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Q: ketch the surface 13zS 19-x² - y' and x'+y' <1

A: To sketch the graph:

Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: Determine if the surface x^2 + y^2 +z^2 = 1 is tangent to the surface x^2 + y^2 + z^4 = 1 at…

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Q: Determine the surface area obtained when the curve with parametric equations x = 4t, y=t^3,  0 < t…

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Q: Determine the following: (a) the general equation of the tangent plane to the surface at Po (b) the…

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Q: If z = f (x, y) is a smooth continuous surface such that f.(a,b) =0 and f,(a,b) =0 then what can you…

A: Please see the explanation below

Q: Determine the area of the parametric surface S with equation R(u, v) = (u²+v², 2uv, u² −v²), where 0…

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Q: Find the unit normal to the surface z=2+2z^2-3y^3 at the point (1,-1,7), pointing down with respect…

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Q: The roof of the Monterrey Campus gymnasium has the shape of the hyperbolic paraboloid given by the…

A: Here we have to use directional derivative  Directional derivative of a function f(x,y,z) in the…

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Find the equation of the tangent plane to the given surface at the specified point   2x=y^2+z^2-9 at…

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Q: The exact solution of the 2q(z - px - qy) = 1 + q^2 equation and by using this solution, Find the…

A: The given equation can be written in the form of the Clairaut's equation as below: z=px+qy+121+q2q…

Q: Calculate SS dxdy D (x+y)² in Surface D limited to curve y=x² and the lines 2 Y=x+2 and x = 1.

A: Given:  integral ∫∫Ddxdy(x+y)2  in the surface D limited to curve y=x2 , y=x+2, x=1  To Find : value…

Q: Use the polar coordinates to find the surface area of the part of the conical surface z^2 = x^2 +…

A: Given conical surface is z2=x2+y2 that lies above the semi-circle y=2-x2

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: Find the extreme values of the function f(x, y, z) = xy + z^2 on the circle in which the plane y - x…

A: Given function is fx,y,z=xy+z2. We have to find the extreme values of the given function on the…

Q: Calculate the geodesic curve of the surface x^2 +y^2 -z=0

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Q: Let f(x, y, z) = x^2 - y^2 – z. Describe the level surfaces.

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Q: Use the cross product to find the area of the (piece of) surface defined as z = ax + by ,      a, b…

A: Formula Used: Area of the surface=∬dAFor r=x i+y j+z(x, y) jdA=|rx×ry|dxdy

Q: Find the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

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Q: Let S be the surface given by the equation x^3+y^3-xz=5. What is the equation of the tangent plane…

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