7. Sketch the surface 15zs9-x' - y² and x'+y' <1

Q: The equation of the tangent plane to the surface x² 8 at the point (-2, 1, 3) is Select one: 1/2…

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Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

A:

Q: 3. Identify and sketch the surface given by z = 16-y²; 0 ≤ y ≤ 2; 0≤x≤ 4. in 3-space, include ALL…

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Q: 3. Find the area of the surface generated from revolving the curve y = x ++4 from x = 1 to x = 2…

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Q: 2) Find the exact area of the surface obtained by rotating the curve about the x-axis. y = /1 + 4x,…

A: We can use the application of integration in order to solve the given problem.

Q: 5. Find the area of the surface obtained by rotating the curve about the x-axis: x' + 6. 1 <x<1 1 2x

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Q: Classify all critical points for the surface flaiy)= 2x-y-2xy.

A: We have to classify all the critical points for the surface…

Q: Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved…

A: Use the formula of arc length to determine its length. Now use to it determine the volume generated…

Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

A:

Q: 14) Find the points on the surface xy- z2 = 1 that are closed to the origin. %3D

A: To find the point on the below surface that is closed to the origin. xy−z2=1

Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: (7.5.0)- Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point %3D

A: Given F(x, y, z)=z-sin(x-2y) ∂∂xF(x, y, z)=∂∂x(z-sin(x-2y))=-cos(x-2y)∂∂yF(x, y,…

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: Find a unit normal to the surface x'y + 2xz = 4 at the point (2,-2,3).

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Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: .Find the area of the surface generated from revolving the curve y = x3 ++4 from x = 1 to x = 2…

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: Find the area and centroidal distances of the curve that lies between the equations y=4-x^2 and…

A: Consider the region bounded between the curves is as shown in the figure below: Here, the objective…

Q: Find the surface area of revolution of x=y2 about the y-axis at [0,2]. Graph.

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Q: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

A:

Q: Find a set of symmetric equations for the normal line to the surface xyz = 12 at the point (2, −2,…

A: The normal line to the surface xyz = 12 at the point (2, −2, −3).

Q: 3. Find the area of the surface generated from revolving the curve y =x++ 4 from x 1 to x 2 about…

A: Given, Curve ,y=x33+14x+4 To find : Area of surface generated after revolving the given curve from…

Q: 4. Find the area of the surface obtained by rotating the curve x²/3 + y>/3 = 1, 0 <y<1 about y-axis.

A: If the curve defined by the parametric equations x=x(t), y=y(t)  with a≤t≤b , is rotated about the…

Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: 4) Find the families of lines of curvature of the surface : =+ y² .

A: Given: z=x2+y2

Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Suppose that the curve y =( x^4)/8 + 1/(4x^2) on the interval [1, 2] was revolved about the x-axis.…

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Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: 4. Parameterize the curve of intersection of the surfaces z = x² + y² and y² + (z – 1)² = 1.

A: parameterisation

Q: y = N|XW --- - 6x 1 <x<1

A:

Q: 5. Find the area of the surface of revolution generated by revolving .3 y = on interval [0,3] about…

A: Given: The function y=x33on interval 0,3, To find: The area of the surface of revolution generated…

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

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Q: Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

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Q: :y² + z² — ² by first sketching at least three cross sections in each of the 4. Graph the surface 1…

A: A quadric surface is a graph of an equation in the three variables x, y and z in a three dimensional…

Q: Find the points on surface z^2=xy+4 closest to origin.

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Q: 6. Find the area of the surface formed by revolving about the curve defined by y = x2 - x2, 1<x<3…

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Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: 5) Consider the surfaces S1 : ryz = 10 and S2 : z =r² + y and the %3D point Po = (1,2,5).

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Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

Q: Sketch the section of the surface at x = 0. y - 252 = 25 -12- -8 12 -6 -4 -6 12 -4 -8 -12 6 4 4 -6-4…

A: topic - hyperbola y2-25z2= 25 is a hyperbola with vertex are (0,5,0) and (0,-5,0)

Q: Find the surface of revolution of the curve y = 4 + 3x² that is rotated about the y- axis between 1…

A: We have to find the area of the surface of revolution of the curve y=4+3x2 that is rotated about the…

Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. y = x3/3, 0 ≤…

A:

Q: (#2) Find the area of the surface generated by revolving the curve about x-axis for f(x) = 2Vx on…

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Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,