Which of the following conditions will make the (yーk)? (xーh)? equation a2 (z-1)? = 1 an equation of a sphere in xyz-space O a = b = c O a b >c

Q: Sketch the section of the surface at y = 0. 2x + z = 3 4 -8 -6 -4 2/4 -2 6 8 -6 -8- 6. AM -8 -6 -4-…

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

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Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

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Q: Sketch the surfaces PARABOLOIDS AND CONES z = 8 - x2 - y2

A: Consider the equation of the surface, z = 8 - x2 - y2

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: A funchion is defined by +the formua a f(x)=Ź ) which of the follauing is the %3D value of

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Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: Find three different parametrizations of the graph of y = x3.

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Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: Sketch the surface: x + 2y + 3z = 12.

A: First find the intersection of plane with axis then draw the plane.

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

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Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

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Q: Find the equation of the tangent plane to the paraboloid z = 2x2 +y? at the point (1,2,6). Select…

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Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = <t, t2>That implies,

Q: Find a parameterization for the quarter sphere x² + y² + z² = a² where z > 0 and x > 0.

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Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

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Q: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

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Q: Let 11 be the surface with the equation = 2√/y+1 and let 12 be the sphere with 2 equation x²+ y²¹+…

A: Solution :-

Q: Explain why C lies on the surface of the cylinder x² + y² = 1.

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Q: Sketch the surfaces PARABOLOIDS AND CONES x = 4 - 4y2 - z2

A: The given equation is x = 4 - 4y2 - z2

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

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: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

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Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: Sketch the bifurcation diagram for y = (A– 4t)y (where A is a parameter, as usual). 2

A: To find- Sketch the bifurcation diagram for y' = λ - 4t2y (where λ is a parameter, as usual)

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

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Q: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: Find the equation of the tangent plane to the surface 9x +36y +4z? = 108 at the point (-2,1,-3).…

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Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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Q: The semi-hyperbola H(X)=(sqrt(x^2-1)) is continous at which x interval?

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Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Sketch the xy-trace of the sphere whose equation is (x+3)2 +(y−1)2 +(z−3)2 =18.

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Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: Find the equation of the sphere of radius 7 centered at (3, 5, 3). O (x – 3) + (y– 5 + (z - 31 = 7 O…

A: Let's find.

Q: Find the flux of F = z²k upward through the part of the sphere x² + y² + z² = a² in the first octant…

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Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: Plot the implicitly given surface (x − 1)² /4 + (y − 1)² +z² = 1 (a) using the sphere function. (b)…

A: As per the question we have to plot the following surface : (x-1)2/4 + (y-1)2 + z2 = 1 With the help…

Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

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Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

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Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Q: Find the points on the surface xy – z2 = 1 that are closed to the origin.

A: Given surface is xy-z2=1. let xy-z2-1=0⇒z2-xy+1=0 Now distance from origin is…

Q: Find the points on the surface 2 2 xY + 100 that are closest to the origin.

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