Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

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: 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 portion of the paraboloid given by the equation z = 1– x2 – y² that is…

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Q: Sketch the surface.......... ASSORTED ............... x2 + z2 = 1

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Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

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Q: Classify the surface: 1-z = 3y? + 4z? ,2

A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

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: What is the equation of the surface revolved about the x-axis for z² - xz = ln x + 3x? A. y² + z² =…

A: Given: The equation of surface which is z2-xz=lnx+3x. This equation is a quadratic equation for z.…

Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

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 exact area of the surface obtained by rotating the curve about the  x-axis.   x = 1/3 ( y2…

A: Given curve is x=13y2+232 over 1 ≤ y ≤ 2. The exact area of the surface obtained by rotating the…

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: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

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: sketch the given surface. x2 − 4y2 = z

A: Given: x2-4y2=z Divide the equation both sides by 4. x24-4y24=z4x222-y21=z4 The equation…

Q: Find the shortest distance between the surface z = x² + y² and the plane r + y – z = 4.

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Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: Classify the surface: 1 – x = 3y + 4z?

A: Given :  The surface 1 - x = 3y2 + 4z2.   To classify the given surface.

Q: Find the area of the surface cut from the paraboloid x2 + y + z2 = 2 by the plane y = 0.

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

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

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Q: Consider the portion of the plane x + 2y + 3z = 12 that sits above the circle (x − 2)^2 + (y − 2)^2…

A: The solution are next step

Q: Sketch the section of the surface at y= 0. 4. + 9 36

A: Given the equation4x2+9z2=36

Q: If the maximum distance from the surface x? + 2y² + z? = 3 to the point (1,0, –1) is Va+ bv6, what…

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Q: Sketch the surface r = 2y? + 32².

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

A: Given: x2 + y2 − z 2= 1

Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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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: Compute the surface area of the ellipse that lies on the plane z = 11 – 3x + 2y and inside the…

A: The surface area of the surface given by z=f(x,y) where (x,y) is a point from the region D in the…

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: Q3/ Sketch the surface z 3x2 + y? +1 and find its linear approximation at P.(0,-1).

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

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Q: Q4(a) Find the surface area of the part of the paraboloid z=10-x -y' that lies above the plane :=1.

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

A: Solution-

Q: Sketch the portion of the surface that lies in the first octant: y = z. 0.15 0.a 0.1 0. 0.15 0.18

A: To sketch the portion of the surface y=z that lies in the first octant. The sketch of y=z is:

Q: Classify and Sketch the surface X2+ Zy² + Z? -4x+4y-2z+3:0

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

Q: Find the slopes of the surface in the x- and y-directions at the given point.

A: It is given that,z=xy  and point (1,2,2). We have to find the slopes of the surface in the x- and…

Q: Sketch the section of the surface at y = 0. z = V4 +x² + y? 6 6 -8 -6 -4 -2 -2 -5-4-3--1, -8 -6 -4…

A: Given query is to the graph of the given expression.

Q: Sketch the surfaces 1. z = y2 - 1 2. 4x2 + y2 = 36

A: Using graphing calculator to sketch themz=y^2-1

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

A: Solution

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: Sketch the section of the surface at y = 0. z = 6r 4 2 -6 -4 -2 6. -4- -6 6r 4 2 -6 -4 -2- -4 4. 2.…

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Q: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

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Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

Q: ii) Find the exact area of the surface obtained by rotating the curve y = x³ + 1 ≤ x ≤ 2, 1 3 12x 9

A: Use Area of surface  formula.