Find the minimum distance from the point to the surface z = V7 - 2x – 2y. (Hint: To simplify the computations, minimize the square of the distance. (-2, -2, 0)

Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

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

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: Find the area of the surface formed by revolving the portion in the first quadrant of the graph of…

A: Rearrange the given equation to find y in terms of x and thus f(x). Plot the curve and find the…

Q: Sketch the region in the xy-plane defined by the equation or inequalities. (a) -1sys3 (b) |지 < 4 and…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Find the points on the surface y2 36 + xz that are closest to the origin. (х, у, 2) (smaller…

A:

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x +…

A: Use Lagrange multipliers to find the shortest distance from the point (2, 0, −6) to the plane x + y…

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: Find the greatest and smallest values that the function f(x, y) = 4x+5y takes on the circle x2 + y?…

A:

Q: Find the points on the surfaces z = V² + y? and z = 2 – x/2 having the shortest distance to the…

A: We know that the two given surfaces will intersect at some curve whose equation can be obtained by…

Q: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

A: Find the minimum distance from the point (4, 0, 6) to the plane x − y + z = 3.

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

A:

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

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

A:

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

A:

Q: A5: What is the minimum (perpendicular) distance from the point p = (-1,–2) to the line L := 4x = 14…

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 8x – 6y on the circle…

A:

Q: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

A: Find the distance using distance formula and then differentiate to get the minimum value equate the…

Q: The area, in square units, bounded by the curves y = x² , y=2 – x and y=1 is ,

A: For a bounded figure, to find the area we need to determine the limits and the curves we need to…

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

A:

Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: · What is the shortest distance from the surface xy + 6x + z = 41 to the origin? distance =

A: The surface is given as , xy+6x+z2=41 find the shortest distance from the surface to the origin.

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: Find the minimum distance from the point (-6, -6, 0) to the surface z = O√√559 O 3√61 09 O√773 O√69…

A:

Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

A:

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

A:

Q: Find the point on the parabola x = t, y = t²,-∞ < t < ∞o, closest to the point (2, 1/2). (Hint:…

A:

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: Use Lagrange multipliers to find the minimum distance from the Curve Point Parabola: y = x² (0, 3)

A: Given: The parabola y=x2 and indicated point is 0,3 Formula for the distance is d=x1-x22+y1-y22…

Q: Find the minimum distance from the point to the plane x - y + z = 9. (Hint: To simplify the…

A:

Q: Use LaGrange multipliers to find the minimum distance between the origin and the plane x+2y+3z=28.

A:

Q: Find the point on the graph of z = x2 + y2 + 10 nearest the plane x + 2y - z = 0.

A:

Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

Q: find the points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

A:

Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: Find the minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

A:

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

A:

Q: Find the minimum distance from the surface to the given point. (Hint: Start by minimizing the square…

A: The minimizing function is, d2=(x-8)2+y2+z2

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: Find the shortest Distance d faumthe point to the plane X+y+Z=8.

A: Let's find.

Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: nd the minimum distance from the point to the surface z = V7- 2x - (-2, -2, 0)

A:

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

A:

Q: Evaluate the length of the curve y = 3 + 3Vx +1 , 0<x< 3

A:

Q: Find the points on the surface 2 2 xY + 100 that are closest to the origin.

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.