For the surface a?+ - z = 1, a curve in a form of a parabola can be formed bi passing through a plane parallel to the xz plane O xy plane

Q: Consider the rormal line to the surface z= z + y? (parabokoid) at the point P(1,1, 2) Find the point…

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Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

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Q: Find the surface area of the paraboloid z= 1 - (x2 + y?) that lies between the sphere x? + y? + z² =…

A: Given the region

Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

A: Given equation of curve is z = ln x The radius function about z axes is  r(z) = x = ez

Q: (b) Sketch the trace of the surface z = 2x? – y? when x = -1. Label your axes, and give the…

A: Given surface is  z=2x2-y2          (i) By putting x=-1 in (i), the surface becomes z=2-y2 The graph…

Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

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

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

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Q: Which of the following is not a parametrization of the parabola y = ² ? O x = vt, y =t O x = t, y…

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Q: - Graph the surface 1 = y² + z² — by first sketching at least three cross sections in each of the xy…

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: a) Evaluate x²y? ds, where the curve C is the intersection between the surface z = := V1– y? and the…

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Q: Answer the following neatly and completely. 1. Find the point P such that =r, where A(4,3, –2),…

A: Given : z = x2 + 4y2.   To identify the quadric surface and to sketch the graph of z = x2 + 4y2.

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: Consider the surface S: Z=4x²+5y?, an equation of the plane fangent to S fhe point P(-2,1, 21) is…

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Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: te the surface integral /| (32zi + 2zyj+ 2yzk) · ds S is the part of the parabola z = 15 – x² – y…

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Q: Determine the projection of the following surface on the xz plane. (xz trace) 4z – + = 0 O Parabola…

A: Solution is given below:

Q: Determine the projection of the surface – y? = z on the yz-plane? (Hint: a = 0) Circle O No answer…

A: The solution 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: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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Q: Find all points on the surface given below where the tangent plane is horizontal. z = 5x - 6xy - 5y…

A: We know the slope of the horizontal tangent plane is zero. So we can put ∂z∂x=0 and ∂z∂y=0.

Q: The equation of the tangent plane to the surface yey +z =0 at the point (0,-1,1) is az+by+cz = 1.…

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Q: 6. Consider the sphere a2 + y? + (z-3)2 = 1. Find the point P (a, b, c) on the sphere such that the…

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Q: Identify a generating curve on the xz-plane for the surface of revolution with equation a² + y? + 2?…

A: Consider the surface of revolution with equation, x2+y2+z2=e2x it is required to find the generating…

Q: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+4)

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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: For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola.…

A: We have been given the equation  4x² + y² −z = 0           (1)

Q: Determine the projection of the following surface on the plane of the xy-axes -2y? + + =1 3 3 O…

A: -2y2+x23+z23=1To find the projection

Q: 3. Use polar coordinates to find the surface area of the paraboloid z = x² +y² – 5 that lies below…

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Q: The tangent plane to the graph of the surface z=in(x2+y?} at the point (1,0,0) contains point…

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Q: Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+ 4)

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Q: a) Evaluate y° ds, where the curve C is the intersection between the surface z and the plane x = 3…

A: Integration problem...

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: Find the points on the surface 2a2+ ly? + 522 = 1 at which the tangent plane is parallel to the…

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Q: 1. Find a parametric representation for the surface: the part of the sphere x2 + y? + z2 = 4 that…

A: According to the given information, It is required to calculate the parametric representation for…

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y² + z? = = 24 and the…

A: We have to write the intersection curve

Q: Consider the surface z = 4x2 + y? + 1. An equation for the tangent plane to this surface at the…

A: Let fx,y=z. Differentiate the function f(x,y) partially with respect to x and y, to find fx and fy .…

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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Q: What are the reace curves of this surface for x=0, y=0, and for z=k? Name the shape of the surface.…

A: Note : In the question it has to be '' trace curves '' instead of '' reace curves ''. So, we are…

Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

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

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Q: The tangent plane to the graph of the surface z-In(x<+y) at the point (1,0,0) contains point (3,3,t)…

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Q: Which of the following represents a plane surface whose x-, y-, and z-intercepts are a, b, and c…

A: Given questions are solved.

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

A: Solution

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

A: and point (1,0,0)

Q: Identify the surface by completing the squares. x + 4y? – 2 – 6x + 8y + 4z = 0 O An elliptic…

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Q: (3) Consider the quadric surface S C R, having equation a2 + y? - z2 = 9. Find all lines through P…

A: General equation of line from point 3,-3,3 is x,y,z=3,-3,3+tl,m,n.  Substitute it in the quadratic…

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

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