Sketch the surface z = f(x,y). f(x, y) = -x 2 - y 2 USE GEOGEBRA

Q: Find the equation of the tangent plane to the surface y = 2x2 - z at the point %3D (0, -1,-2) y+2z =…

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Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: Find the surface are generated when y= (x^3)/5 is revolved about the x axis on the interval…

A: Explanation of the solution is given below...

Q: How do you calculate the area of a parametrized surface in space? Of an implicitly defined surface…

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Q: Find the slope of the tangent line at the point (1,−2,−3) on the curve of intersection of the…

A: Given surface is z=5-4x2-y2 The slope of tangent line to the curve that is the intersection of the…

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: Sketch the surface z = f(x.y). f(x.y) = - /x² +y?

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Q: Describe and sketch the surface (x2/16) + (y2/9) + z2 = 1

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Q: Find the area of the surface obtained by rotating the curve y = 4x + 4, 0 < x< 8, about %3D the…

A: To find- Find the area of the surface obtained by rotating the curve y2 = 4x + 4, 0 ≤ x ≤ 8, about…

Q: Find an equation which describes the surface created by rotating (r, x, 0) around the r-axis. Note…

A: Our Aim is to find an equation which describes the surface created byrotating (x,x,0) around the…

Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 16 – x – y.…

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: Find the area of the surface. The part of the surface y = 4x + z2 that lies between the planes x =…

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Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Find the equation oftangent plane and normal lines ofthe surface: f(x,y, z) = 10x² –14 y² +11z³-7 at…

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

A: Given, z=9-x2-y2

Q: Classify the surface: 1- x = 3y? + 4z2 O Plane O sphere O cone O Elliptic paraboloid O Ellipsoid

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y² and z = 25 – x – y².…

A: Given that: z=x2+y2      ......(1)z=25-x2-y2      ......(2)

Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: Sketch the surface z = f(x,y). f(x.y) = 4x² + 4y² + 2 OC. OD.

A: Given function is fx,y=4x2+4y2+2. We have to sketch the surface of fx,y=4x2+4y2+2.

Q: Find the equation of tangent plane and normal lines of the surface: f(x, y, z) = 5x² + 4 y2 +z³-9 at…

A: Here we have to find the equation of the tangent plane and normal lines of the surface:…

Q: Find a parametrization of the curve. The intersection of the surfaces z = x^2 − y^2 and z = x^2 + xy…

A: Given : The surfaces z = x2 - y2 and z = x2 + xy - 1.   To find the parameterization of the curve.

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: Find the area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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Q: Evaluate the surface z =1,0<x,y <1.

A: To solve this we will use divergence theorem.

Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: The two surfaces x2 + y2 + z2 = 6 and 2x² + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: Given: The two surfaces  x 2 + y 2 + z 2 = 6  and  2 x 2 + 3 y 2 +  z 2 = 9. The given two surfaces…

Q: Sketch the surface of f(x,y)

A: To sketch the function

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: 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 the surface revolved for the x-axis is, z2-xz=ln(x)+3x

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

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Q: Find the equation of tangent plane to the surface x² + 2y? + 3z2 = 21 which is parallel to the plane…

A: Topic- equation of tangent to surface

Q: Find the tangent plane at the point (1,-1,1) of the surface f(x,y,z)= x^2y+y^2z+z^2x. %3D

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Q: Þ(x, y, z) = e¬x²-y²-z²+2yz

A: We have to solve given problem:

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,27). y = sinx 4 56 1 3. 6…

A: The given equation of the curve is: y=sinx To draw the given equation on the x-y plane we need to…

Q: Classify the quadric surface. −49x2 + y2 + z2 = 49

A: Given query is to find the shape of the surface.

Q: Let the surface xz – yz³ + yz? = 2, then - the equation of the tangent plane to the surface at the…

A: Equation of tangent plane of the surface f(x,y,z) =0 at (x0,y0,z0) fx (x0 ,y0 ,z0 )(x-x0) +fy (x0…

Q: Let S be the surface given by the equation x^3+y^3-xz=5. What is the equation of the tangent plane…

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Q: area of the surface obtained by rotating the curve y=x^3, x ∈ [0

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Q: The area of the surface obtained by rotating the curve y = V9-x2, -3 < x < 3 about the x-axis is

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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: Find a parametrisation of the curve of intersection of the surfaces: x^2 + 2y^2 + z^2 = 5 and x^2 +…

A: This is parameterisation of curve problem

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

Q: Find the equation of tangent plane to the surface x? + 2y? + 3z2 = 21 which is parallel to the plane…

A: equation of the tangent surface of  F= x2+ 2y2+ 3z2= 21   which is also parallel to the plane…

Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

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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: Use  inertia  to  classify  the  quadric surface  given by equation. x2 + y2 + 2z2 − 2xy − 4xz − 4yz…

A: We have to use  inertia  to  classify  the  quadratic surface  given by equation. x2 + y2 + 2z2 −…