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If u=x^2+y^2+z^2, v=xy+yz+zx, w=x+y+z find the value of Jacobian J del(u,v,w)/ del(x,y,z) Question Question If u=x^2+y^2+z^2, v=xy+yz+zx, w=x+y+z find the value of Jacobian J del(u,v,w)/ del(x,y,z) Jacobian matrix problems If u=yz/x, r=zx/y, w=xy/z, Show that J [(u, v, w)/ (x, y, z)] =4 If u=x+3y^2, v=4x^2 yz, w=2z^2-xy, Evaluate del (u,v,w)/del (x,y,z) at the point (1,-1, 0) If u=(x_2 x_3)/x_1, v=(x_1 x_3)/x_2, w=(x_1 x_2)/x_3 find the value of Jacobian J del (u,v,w)/del(x_1,x_2,x_3) If u=x^2+y^2+z^2, v=xy+yz+zx, w=x+y+z find the value of…

If u=(x_2 x_3)/x_1, v=(x_1 x_3)/x_2, w=(x_1 x_2)/x_3 find the value of Jacobian J del (u,v,w)/del(x_1,x_2,x_3) Question Question If u=(x_2 x_3)/x_1, v=(x_1 x_3)/x_2, w=(x_1 x_2)/x_3 find the value of Jacobian J del (u,v,w)/del(x_1,x_2,x_3) Jacobian matrix problems If u=yz/x, r=zx/y, w=xy/z, Show that J [(u, v, w)/ (x, y, z)] =4 If u=x+3y^2, v=4x^2 yz, w=2z^2-xy, Evaluate del (u,v,w)/del (x,y,z) at the point (1,-1, 0) If u=(x_2 x_3)/x_1, v=(x_1 x_3)/x_2, w=(x_1 x_2)/x_3 find the value of Jacobian J del (u,v,w)/del(x_1,x_2,x_3) If u=x^2+y^2+z^2,…

If u=x+3y^2,  v=4x^2 yz, w=2z^2-xy, Evaluate del (u,v,w)/del (x,y,z) at the point (1,-1, 0) Question Question If u=x+3y^2,  v=4x^2 yz, w=2z^2-xy, Evaluate del (u,v,w)/del (x,y,z) at the point (1,-1, 0) Jacobian matrix problems If u=yz/x, r=zx/y, w=xy/z, Show that J [(u, v, w)/ (x, y, z)] =4 If u=x+3y^2, v=4x^2 yz, w=2z^2-xy, Evaluate del (u,v,w)/del (x,y,z) at the point (1,-1, 0) If u=(x_2 x_3)/x_1, v=(x_1 x_3)/x_2, w=(x_1 x_2)/x_3 find the value of Jacobian J del (u,v,w)/del(x_1,x_2,x_3) If u=x^2+y^2+z^2, v=xy+yz+zx, w=x+y+z…

If u=yz/x, r=zx/y, w=xy/z, Show that J [(u, v, w)/ (x, y, z)] =4 Question Question If u=yz/x, r=zx/y, w=xy/z, Show that J [(u, v, w)/ (x, y, z)] =4 Jacobian matrix problems If u=yz/x, r=zx/y, w=xy/z, Show that J [(u, v, w)/ (x, y, z)] =4 If u=x+3y^2, v=4x^2 yz, w=2z^2-xy, Evaluate del (u,v,w)/del (x,y,z) at the point (1,-1, 0) If u=(x_2 x_3)/x_1, v=(x_1 x_3)/x_2, w=(x_1 x_2)/x_3 find the value of Jacobian J del (u,v,w)/del(x_1,x_2,x_3) If u=x^2+y^2+z^2, v=xy+yz+zx, w=x+y+z…

Show that Z (x, y) =x^3+y^3-3xy+1 minimum at (1,1) Question Question Show that Z (x, y) =x^3+y^3-3xy+1 minimum at (1,1) Maxima and Minima Problems Find the maximum and minimum values of the function x^3+3xy^2-15x^2-15y^2+72x Examine the function f (x,y) =x^4+y^4-2 (x-y) ^2 for extreme values Show that Z (x, y) =x^3+y^3-3xy+1 minimum at (1,1)

Examine the function f (x,y) =x^4+y^4-2 (x-y) ^2 for extreme values Question Question Examine the function f (x,y) =x^4+y^4-2 (x-y) ^2 for extreme values Maxima and Minima Problems Find the maximum and minimum values of the function x^3+3xy^2-15x^2-15y^2+72x Examine the function f (x,y) =x^4+y^4-2 (x-y) ^2 for extreme values Show that Z (x, y) =x^3+y^3-3xy+1 minimum at (1,1)

Find the maximum and minimum values of the function x^3+3xy^2-15x^2-15y^2+72x Question Question Find the maximum and minimum values of the function x^3+3xy^2-15x^2-15y^2+72x Maxima and Minima Problems Find the maximum and minimum values of the function x^3+3xy^2-15x^2-15y^2+72x Examine the function f (x,y) =x^4+y^4-2 (x-y) ^2 for extreme values Show that Z (x, y) =x^3+y^3-3xy+1 minimum at (1,1)

Find the dimensions of the rectangular box open at the top of maximum capacity whose surface is 432 sq.cm Question Find the dimensions of the rectangular box open at the top of maximum capacity whose surface is 432 sq.cm Solution Question Find the dimensions of the rectangular box open at the top of maximum capacity whose surface is 432 sq.cm LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy…

Find the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid x^2/a^2 +y^2/b^2 +z^2/c^2 =1 Question Find the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid Solution Question Find the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid x^2/a^2 +y^2/b^2 +z^2/c^2 =1 LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and…

Show that the rectangular box of maximum value and a given surface area is a cube. Question Show that the rectangular box of maximum value and a given surface area is a cube. Solution Question Show that the rectangular box of maximum value and a given surface area is a cube. LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and minima values of the function…

A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum Question Question A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and minima values…

If x, y, z are the angles of a triangle, find the maximum value of sin x sin y sin z Question Question If x, y, z are the angles of a triangle, find the maximum value of sin x sin y sin z LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and minima values of the function f (x, y) =3x+4y on the circle…

Find the maximum and minimum values of x^2+y^2 subject to the condition 2x^2+3xy+2y^2=1 Question Question Find the maximum and minimum values of x^2+y^2 subject to the condition 2x^2+3xy+2y^2=1 LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and minima values of the function f (x, y) =3x+4y on the circle x^2+y^2=1 using method of Lagrange’s multipliers Find the maximum and minimum values of x^2+y^2 subject to…

Find the maxima and minima values of the function f (x, y) =3x+4y on the circle x^2+y^2=1 using method of Lagrange’s multipliers Question Question Find the maxima and minima values of the function f (x, y) =3x+4y on the circle x^2+y^2=1 using method of Lagrange’s multipliers LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and minima values of the function f (x, y) =3x+4y on…

Discuss maximum or minimum for x^3+y^3-3xy Question Question Discuss maximum or minimum for x^3+y^3-3xy LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and minima values of the function f (x, y) =3x+4y on the circle x^2+y^2=1 using method of Lagrange’s multipliers Find the maximum and minimum values of x^2+y^2 subject to the condition 2x^2+3xy+2y^2=1 If x, y, z are the angles of a triangle, find…

Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Question Question Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 LaGrange's Method Problems Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2 Discuss maximum or minimum for x^3+y^3-3xy Find the maxima and minima values of the function f (x, y) =3x+4y on the circle x^2+y^2=1 using method of Lagrange’s multipliers Find the maximum and minimum values of x^2+y^2 subject to the condition 2x^2+3xy+2y^2=1 If…

If z(x+y) =x^2+y^2, Show that (del z/del x – del z/del y) ^2= 4(1- (del z/del x)-(del z/ del y)) Question Question If z(x+y) =x^2+y^2, Show that (del z/del x – del z/del y) ^2= 4(1- (del z/del x)-(del z/ del y)) Total Derivatives Problems Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives. Find du/dt if u=xy+yz+zx and x=t cost , y=tsint , z=t @ t=π/4 If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x If…