Given the surface of z =10-4x² – y² : Sketch the surface of z=10-4x² – y² where z>0 and show the traces at planes planes x=1 and y=2, respectively.

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: If (a,ß.r) is a point at which the surface x2+y2-z-2x+42=0 has a horizontal tangent plane, then Iyl=

A: Horizontal tangent plane

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: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: (c) The cone r² = 4(y² + z?) for (0 <x < 4

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Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: We need to determine the equation of the surface that is obtained by rotating the line z=7y about…

Q: Find the points on the surface x² −yz = 5 that are closest to the origin.

A: Let the point P be (x,y,z). The distance between the point P and origin is given by the formula…

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 - Select a correct name for this surface and point…

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Q: Find the points on the surface x2 - zy = 4 closest to the origin.

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Q: Consider the normal line to the surface z = x2 + y² (paraboloid) at the point P(1, 1, 2). Find the…

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Q: Find the area of the surface. The part of the paraboloid z = 1 − x2 − y2 that lies above the plane…

A: Given that the part of the parabola z=1-x2 -y2 that lies above the plane z= -6 . Here we have to…

Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: Determine the projection of the following surface on the xy plane. (xy trace) 4z-목 + =0

A: here first solve the given surface and then we trace it

Q: Consider the surface z = 2 – xy in R³. Use the second derivative test to find the points on this…

A: Given curve z = 2-xy To find :- Use the second derivative test to find the points on this surface…

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: The attached figure shows the surface S1: y + z= 2, limited in the first octant with surface S2: x =…

A: The area of a surface z=f(x,y) bounded by the region R is given by the integral expression:-…

Q: For the surface 4x² +2²-y²=9, classify the trace when z = 1. O line O hyperbola O ellipse O parabola

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Q: Find the area of the portion of the surface z = 8x+4y that lies above the triangular region with…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

A: Solution is given below:

Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…

A: The given quadratic surface is  x2+y42+z2=1 , y=0

Q: Given a surface 2xy - In (3z- 2) = 10, wherez=f(x, y). Find zx at y =7, z= 1. Leave your answer…

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Q: For the surface described by z= - 20y+x² – 10x +3y-2xy | a. At what point are both zx=0 and zy=0 %3D…

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Q: Sketch the surface r = 2y? + 32².

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Q: Given a surface 2xy - In (5z - 2) = -10, where z = f(x,y). Find Zx at y = -10, z = 1. Leave your…

A: Partial differentiation

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

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Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

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: Let S be the surface with equation (z - 4)² = 4x² + 4y². Viewing S as a surface of revolution, find…

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Q: Evaluate [[. (y+210 – = )aS, where S is the surface cut from the paraboloid y² +4z = 36 by the…

A: Surface integral of a function f(x,y,z) on a surface S given by z=g(x,y) ∫∫Sf(x,y,z)dS = ∫∫Df(x,y,…

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

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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) O x- y + ez…

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Q: Let f(x,y)=/4– 4x² – y² . Find its domain and give a rough sketch of its surface.

A: The given function is:fx, y=4-4x2-y2To find domain and sketch the surface

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: Graph the surface 1 = y? +z? - by first sketching at least three cross sections in each of the xy…

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Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

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Q: Given a surface 3xy - In (3z - 2) = -5, where z = f(x,y). Find zx at y = 3, z = 1. Leave your answer…

A: This question is based on Partial differentiation of function

Q: Given a surface 5xy - In (2z - 5) = -1, where z = f(x,y). Find zx at %3D = -9, z = 1. Leave your…

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Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + Z?…

A: Solution-

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

Q: The surface x2 + y² = z² is identified as O A. Paraboloid O B. Cone O C. Hyperboloid of one sheet O…

A: the correct answer is option: D .) Hyperboloid of 2 sheets

Q: Find a set of parametric equalions for the surface formed when the curve y(1+z²) – 1 = 0 is revolved…

A: Find a set of parametric equations for the surface formed if the curve y1+z2-1=0 is revolved about…

Q: Find the area of the portion of the surface x2 - 2z = 0 that lies above the triangle bounded by the…

A: Definition used:

Q: Identify and sketch the section of the surface at z = 0. v2 = 1 25 4 16 Type of the surface: too 4 4…

A: Solve the given

Q: Consider the surface given by the equation z - y = x2. Draw a total of at least 3 traces in at least…

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Q: Determine the sections of the following surface on planes parallel to the xz plane. -y+ = 1 %3D O…

A: here first we solve for the surface and then check it .

Q: Find the exact area of the surface obtained by rotating the curve abo = V7 - x, 1<x< 7

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Q: Use traces to sketch and identify the following surface 25x2+4y2+z2=100

A: Ellipse is a closed curve around 2 focal points such that for every point on that curve, the sum of…

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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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.