#3. Find the point on the surface x2 + 2y + z = 3 that is closest to the point P = (-1,3,2). You can assume that such a point exists.

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: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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Q: Identify and sketch the surfaces x2 + y2 - z2 = 4

A: Given, The surface is x2 + y2 - z2 = 4

Q: Suppose f(x, y, z) = In(7x + 9y+7z). Find an equation for the level surface of f that passes through…

A: Given Data: The level of the curve for fx,y,z=In 7x2+9y+7z2 is of the form,…

Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin²z, z = [0, π]

A: Any point on the 3D plane is represented using the ordered pair: x, y, z. A graphing utility can be…

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 z2-xz=lnx+3x which is of surface and is quadratic for z.  To find: The equation…

Q: Find the equation of the plane tangent to the following surface at the given points. x² +…

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Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

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

A: To Plot: Graph The Surface 1=y2+z2-x24 by plotting at least three cross section in xy and yz plane

Q: Find the points on the surface x2 - zy = 4 closest to the origin.

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

A: Graph the surface by using a 3D graphing calculator like desmos. Three cross sections in xy plane…

Q: sketch the given surface. x2 − y2 + 9z 2 = 9

A: Given, x2-y2+9z2=9

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 of the plane tangent to the following surface at the given point. z = 6 - 4x2 - y2;…

A: By using equation of tangent plane for surface, we calculate the required tangent plane.

Q: 3. Consider Hhe following two surfaces. 8x-54-82 = -13 a) Show that the surdaces intersect at the…

A: Given surfaces are  z=2 xy2 and 8x2-5y2-8z=-13 (a)  Let fx,y,z=z-2 xy2=0 Let gx,y,z=8x2-5y2-8z+13=0…

Q: Find the points on the surface z2 = xy + 4 closest to the origin.

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Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: An equation for the tangent plane to the surface (xty at the point P(1, 1, 4) is a) 8r + 8y-:= 0 b)…

A: The given surface is  f(x,y)=z=(x2+y2)2  ...........(1); we have to find the tangent plane at point…

Q: b) If we are at the point (1, 2, 4) on the surface z = xy², and we move a short distance in the…

A: Please check step 2 for solution.!

Q: What is the shortest distance from the surface xy +12x +z^2 =144 to the origin?

A: To find the shortest distance from surface xy +12x +z2 =144  to origin.

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x2 + y? + 22…

A: Solution :-

Q: Sketch the section of the surface at y = 0. 1 + x² + y² Z = 4 -8 -6 -4 -2 4 4 6. 4 -8 -6 -4 -2 2. 4…

A: Given data is: To sketch the surface at y=0 z=1+x2+y2

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

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Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

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: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

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

A: In this question, we want to find the equation of the tangent plane to the given surface.

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 area of the surface generated when the curve f(x) = (2/3)x^(3/2) - (1/2)x^(1/2) ; [1,9] is…

A: Given:

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

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

A: Consider the provided question, We have to find the point on the given surface closest to the point…

Q: Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from…

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Q: Sketch the trace curves of x^2 − y^2 + z^2 − 4x + 2z = 4, and use these trace curves to sketch the…

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Q: 3. (a) Find the equation of the plane tangent to the surface given by f(x, y) = 2xª+2y^+7xy at the…

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Q: Q3. Find the point(s) on the surface xyz 1 closest to the origin. %3D

A: Given: To find the points on the surface xyz=1 is given as,

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

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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: The equation of the tangent plane to the surface a2- 3y2 – 22 +3 = 0 at the point (2, -1, -2) is…

A: We will find the equation of tangent plane m

Q: Find and classify all the critical points of the surface with its equation 2 = 3a²y + y3 – 3x² – 3y?…

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Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

Q: Find and sketch the domain and range of the surface f(x, y, z)= ln(16-4x^2-4y^2-z^2

A: Given: The function is fx,y,z=ln16−4x2−4y2−z2 To determine: We have to find and sketch the domain…

Q: Find the point on the curve of intersection of the paraboloid x – y + 2z = 0 that is dosest to the…

A: Here we have to find the point of intersection of the paraboloid x2+y2+2z=4 and the plane x - y + 2z…

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

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: 2(t3 + 2) Show that the curve x = - ,y = 2t² and z = 3t – 2 3 intersects the surface of x² + 2y² +…

A: Consider the provided question, We have to show that the curve x=2t3+23, y=2t2 and z=3t-2 intersects…

Q: 7. Sketch the surface 1≤z≤2-x² - y²

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