Sketch the 3D graph of the following functions: Surface z= (x-1)² + (y+ 2)² + 3 Surface 4x?+4y²+z²+8y-4z=–4 (i) (ii)

Q: Identify and sketch the surfaces y = - (x2 + z2)

A: Given Data The equation of curve surface is y=-(x²+z²)   The sketch of the surface equation is,

Q: sketch a typical level surface for the function. ƒ(x, y, z) = x2 + y2 + z2

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Q: Describe and sketch the surface x + 2y + 3z = 6

A: Given

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin² z, Z = [0, π]

A: Given.   x^2+y^2=sin^2z

Q: Find the equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25 Sketch…

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Q: Show that the line b2xx1 + a2yy1 - a2b2 = 0 is tangent to the ellipse b2x2 + a2y2 - a2b2 = 0 at the…

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Q: Sketch the graph of the cylinder x (y – 2)² in R³. %3D

A: Solution:   First of all x-y projection of this 3d graph is

Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: Sketch the surface with equation x^2 + y^2 + 2z^2 − 1 = 0.

A: The given equation is x2+y2+2z2-1=0

Q: sketch the graph xyz plane x^2+z^2=4

A: GIVEN: x2 + z2 = 4

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

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Q: A surface has Cartesian equation :- f(xy). given by f(1.9)=6xy-5x -3y+ +7x-6y a) Use any…

A: To graph the function: z=f(x,y) where f(x,y)=6xy-5x2-3y4+7x-6y

Q: Identify and sketch the surfaces x2 + (y - 1)2 + z2 = 1

A: given: the equation of the surface x2+y-12+z2=1

Q: find an equation for the level surface of the functionthrough the given point. ƒ(x, y, z) = √(x - y)…

A: given,  ƒ(x, y, z) = √(x - y) - ln z, (3, -1, 1)

Q: Identify and use traces to sketch the surface 1. y= 9 - x2 - z2 2. y = 4 - z2

A: We will find traces on all 3 co ordinate planes , x=0 ,y=0 and z=0 . then draw the surface  Note :…

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 minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: Name the surface and draw an accurate Graph of x² – y² – z² = 1 in R’.

A: Given: The surface x 2 - y 2 - z 2 = 1     To determine: The name of the given surface and the graph…

Q: Sketch the surfaces 1. x2 + y2 = 4  2. x2 + 4z2 = 16

A: The given surfaces are sketched using online 3D calculator.

Q: Sketch the xy-trace of the sphere whose equation is (x−3)2 +(y−2)2 +(z+4)2 =52.

A: We can find the xy trace by setting z = 0 in the original equation.

Q: Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface…

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Q: An equation for the level surface passing through the point (2,0, - 1) is z =

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Q: Find the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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

A: To identify the surface, set each variable to some constant and find what type of surface produces…

Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

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Q: Q3: Find the points on the surface x^2+z^2-2=0, closest to the origin.

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Q: Identify and sketch the surface by plotting different traces of (x – 1)2 – (x + 2)2 - (z + 4)² = 0.

A: According to the given information, it is required to identify and sketch the surface.

Q: Identify and sketch the surfaces z = - (x2 + y2)

A: Identify and sketch the surfaces z = - (x2 + y2)

Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2 at the point (2,1,-30)

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Q: Q1: Find the maximum and minimum point on the surface f(x,y)= 5xy-7x -y² +3x -6y +2

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Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

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

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Q: Find the slope of the surface z = 3x/y at the point (5,2,15/2) in the x- and y- directions.

A: Given data is: z=3xy  To find the slope of the surface z at the point 5,2,152 in the x and…

Q: Sketch the surface = 2y + 32².

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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: Sketch the surface 1<z</9-x² - y² and x²+y² <1

A: To sketch the given surfaces.

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

A: The objective of the question is sketch the section of the surface at y=0.

Q: Find the point on the surface r² – 2ry + 2y² – x +y = 0 closest to the point (1, 2, –3).

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Q: Find an equation for the plane tangent to the surface z = 2x2 - 7y at the point (3,-1,5)

A: Given surface z=2x2-7y and the point 3,-1,5. The main objective is to find an equation for the plane…

Q: Identify and sketch the section of the surface at x = 0. 4 Type of the surface: 6. 6- 2 -8 -6 -4 4 6…

A: Given the surface

Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: Let f(x, y)=sqrt(2x²+4y² +8) -x. The domain of c for which the level curve f(x, y) = c is an ellipse

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Q: Find the equation of the xy-trace, the equation of the xz-trace and the equation of the yz-trace of…

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Q: Find the equation of the level surface of the function g(x,y,z)=x^2+y^2+z^2-2x+4y-6z corresponding…

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Q: Q1/ Use traces to sketch and identify the surface z2 - 4x2 - y² = 4

A: Let's find.

Q: Sketch the graph of -x + 9y² – 4z² = 36 and identify the surface. %3D

A: Given a function in terms of x, y and z. Here x and y are independent variables and z is a dependent…

Q: Let f(x, y) =V2x²+4y2 +32 -x. The domain of c for which the level curve f(x, y)=c is an ellipse is

A: For the solution follow the next step.

Q: Find the parametric equation of the line of intersection of the planes 2x+y-z=1 and x-2y+3z-9

A: First find cross product take normal vector useformula