1 Find the points have minimum distance From the origih to the Surface xyz =1.

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

A:

Q: Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved…

A: Use the formula of arc length to determine its length. Now use to it determine the volume generated…

Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

A:

Q: c) Find the minimum distance from the point (4,0,6) to the plane x- y +2 = 3

A: The solution is given below. .

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

A:

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: Find an equation of a generating curve given the equation of its surface of revolution. x2 + y2 − 2z…

A: Given equation of surface of revolution is, x2+y2-2z=0

Q: Jategrate h (x.y) = (x+y)i+(-x)j over the closed curve that begins at (-1, 0), goes along the x-axis…

A: we will use green theorem here to solve this question

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

A:

Q: Find the minimum distance from the point to the plane x- y +z = 6. (1, -6, 2)

A:

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

A:

Q: Find the point(s) on the surface xyz = 1 closest to the origin.

A: Given, g(x,y,z): xyz=1 distance from origin is  d=x2+y2+z2 f(x,y,z)=x2+y2+z2  square of distance…

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

A:

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

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: Let L be the line with equation y = x – 1. Find the minimum distance between L and the point (4, 5)…

A: In order to use method of Lagrange multiplier, we first need to find the function to be minimized.…

Q: Which point on the curve y = Vx – 1 + 8 is closest to the point (5, 8)? (x, V) = ( What is this…

A:

Q: 3. Find the radius and center of curvature of the parabola y=x²-4x+4 at any point (x,y)on the curve.

A:

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A:

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

A:

Q: 4) Find the families of lines of curvature of the surface : =+ y² .

A: Given: z=x2+y2

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated poi…

A:

Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

Q: Find the minimum distance from the curve y = 2 to the point P(6,0)

A:

Q: Find minimum perpendecular distance between given paraboles. y = x2 + 1 y = x - x2

A: To find the minimum distance between 2 parabolas

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: Suppose that the curve y =( x^4)/8 + 1/(4x^2) on the interval [1, 2] was revolved about the x-axis.…

A:

Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

A:

Q: Atomic particles with like charges tend to repel one another. Suppose that two beams of like-charged…

A: Here, we can define the path of the given  particle as:

Q: 4. Parameterize the curve of intersection of the surfaces z = x² + y² and y² + (z – 1)² = 1.

A: parameterisation

Q: (a) Find the area of the surface generated by the given curve about x-axis y = V, (b) Find the area…

A:

Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

A:

Q: 6. Find the area of the surface formed by revolving about the curve defined by y = x2 - x2, 1<x<3…

A:

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: find the points of the surface x^2-y^2+z^2=1 which corresponds to the extreme value of…

A:

Q: to Rind the points Lagrange multiplier surface (x-1)(y-2)(Z-)=| near est Qz use on the to the point…

A:

Q: Q/ Find the points have minimum distance from the origin to the surface. xyz²=1

A:

Q: Atomic particles with like charges tend to repel one another. Suppose that two beams of like-charged…

A: x^2 − 4y^2 = 36 is a hyperbola Write it in the standard form and find a and b by comparing.

Q: Find the points on the curve of intersection of the ellipsoid x² + 4y² + 4z² = 4 and the plane x –…

A:

Q: Find the minimum distance from the surface x2 -y2 -z2= 1 to the origin.

A:

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: Find the minimum distance from the point (0, 0, 4) to the surface  z = (1-2x-2y)^1/2   (Round your…

A: Solution:

Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

A:

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to…

A: To Find: Use Lagrange multipliers to find the minimum distance from the curve or surfaceLine : x-y=4…