Identify the following surfaces and sketch. a. x² + 4y² – 4z² – 6x – 16y – 16z + 5 = 0 b. 5y = -z2 + x²

Q: Q2/ Examine the following surface for maximum , minimum, and sa z = x3 – 3x? – 4y2 + 2

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Q: The surface described by the conditions 2 + y? + z² = 4, x 0 is the same as the surface described…

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Q: Identify the surface defined by the following equation. 2x-y²-z² =0

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Q: B- Find all local extreme values of the following surface. f(x, y) = 2xy – x² – 2y? + 3x + 4.

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Q: Sketch the section of the surface at x = 0. y? – 42? = 4

A: Given

Q: Find the ex9ct grea of the Surface obtained by revo lving the Curve f(x)=V5-x for x € (3,5] 9bout…

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

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Q: Find a parameterization for each of the following surfaces: (a) æ² + y² + z² – 4x – 6y = 12 (b) 2x²…

A: We have to find the parametric representation of the following surfaces: x2+y2+z2-4x-6y=12       →…

Q: Sketch the section of the surface at x = 0. y? - 25z? = 25 12 -12 -8 12 -4 -8 -12 4 -6 -2 -4 4.

A: topic - hyperbola

Q: sketch the given surface. x 2+ 9y 2 + 4z 2 = 36

A: To sketch the given graph

Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

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Q: Find the point on the surface z = xy + 1 nearest the origin.

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Q: Express the following equations in standard form to name the corresponding surface and sketch a. x²…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center…

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Q: Describe and provide a rough sketch of the surface determined by the following equation: -x² +4y? -…

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Q: Identify and sketch the surfaces x2 + z2 = y2

A: Given surface is x2+z2=y2. The given equation is in the form of x2a2+z2c2=y2. So, the given surface…

Q: Q3/ Examine the following surface for maximum and minimum points z = 2x2 + 3xy + 4y² – 5x + 2y

A: Since you have posted multiple question according to company rule we are supposed to give solution…

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

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Q: Given the expression x* – 3x + 7 = y³. on the interval [3,5], determine the surface of revolution if…

A: Given; x4-3x+7=y3 on the interval [3,5]

Q: Given the expression x⁴-3x+7=y³ on the interval [3,5], determine the surface of revolution if it is…

A: Given that, the expression is x4-3x+7=y3.

Q: Identify the surface defined by the following equation. y 2 x2 Z= 10 16 The surface defined by the…

A: The given surface represents a Hyperbolic parabola.   A hyperbolic paraboloid is represented as…

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

A: Given the equation4x2+9z2=36

Q: Q5) Find the equation of the surface formed by rotating the following line about the x -axis. 1=…

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Q: Match the equation with the surface it defines. f(x, y) = -√√x²+12 X O O O stisk 3

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: Find an equation for the surface obtained by rotating the line z = 2x about the z-axis. + x²) b. z?…

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Q: Sketch the following surfaces. (a) −9z2 −5y2 −x+4 = 0 (b) 4y2 + 9z2 − x2 = 0 (c) 1−3z2 −y2 −4x2 = 0

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the…

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: sketch the given surface. y 2+ z 2 = 1

A: To sketch: The surface y2+ z2 =1 Concept used: The general equation of the cylinder whose base…

Q: x2 Consider the surface T with equation 4 (y – 3)² + 22 = 1. - 3

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

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Q: (a) x² + 2x + 4y² + 16y + 9z? 19

A: Sketch and identify the surfaces: (a) x2+2x+4y2+16y+9z2=19.

Q: Sketch the surface in R' of the equation presented. x2 + y? - 8x = 0

A: Sketch the graph on xy-plane, i.e., when z=0

Q: Describe the surface given by the equation, and find xy-trace, xz- trace, and yz-trace. 16x2 + 16y?…

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Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 11x ,(z = 0)…

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Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² + y²

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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: What are the reace curves of this surface for x=0, y=0, and for z=k? Name the shape of the surface.…

A: Note : In the question it has to be '' trace curves '' instead of '' reace curves ''. So, we are…

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch on paper.…

A: Express the equation 4y2+z2-x-16y-4z+20=0 in terms of the complete squares of y and z, and then…

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: Identify the following surfaces and sketch your graphic: A)4x² + y²-2y+9Z2-35=0 B)y² + 4z² =x

A: We will standardize  given equations 1st and then find required surface ,

Q: 15r = and o is the surface (x − 3)² + y² + z² = 49 oriented ||r||³ FndS? If F(r): outwards, what is…

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Q: Q2 Find the maXimum and minimum values of aFunction FCXS.2) = 8x+j+ 2 en the Surface x+y, z"=18 %3D

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Q: Find an equation for the surface generated by revolving the curve about the y-axis. y = 2x , (z = 0)…

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Q: If F(r) 17r 3 and o is the surface (x − 4)² + y² + z² = 49 oriented ||r||³ outwards, what is the…

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Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² - y² O O X x

A: Given that       f(x,y) = e1-x^2-y^2