Mathematics Problems

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…

If z = sin (ax+y) + cos (ax-y), Prove that (del)^2 z / del x^2 = a^2 (del)^2 z / del y^2 Question Question If z = sin (ax+y) + cos (ax-y), Prove that (del)^2 z / del x^2 = a^2 (del)^2 z / del y^2 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…

If z=f(x, y) where x=r cos(theta) and y=r sin(theta), Show that (del z/del x)^2 + (del z/del y) ^2 = (del z/del r)^2+1/r^2 . (del z/del (theta))^2 Question Question If z=f(x, y) where x=r cos(theta) and y=r sin(theta), Show that (del z/del x)^2 + (del z/del y) ^2 = (del z/del r)^2+1/r^2 . (del z/del (theta))^2 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…

If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 Question Question If u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 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 u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x,…

If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x Question Question If u=f(x/y, y/z, z/x) prove that p=x/y, q=y/z, r=z/x 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 u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x, y) where x=r cos(theta) and y=r sin(theta), Show…

Find du/dt  if u=xy+yz+zx and x=t cost , y=tsint , z=t  @ t=π/4 Question Question Find du/dt  if u=xy+yz+zx and x=t cost , y=tsint , z=t  @ t=π/4 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 u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x,…

Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives Question Question Find du/dt when u=x^3 y^2+x^2 y^3 with x=at^2, y=2at. Use partial derivatives 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 u=f(x-y, y-z, z-x), Show that del u/del x+del u/del y+del u/del z=0 If z=f(x, y) where…

If v(x,y))=(1-2xy+y^2)^(-1/2) and x del v/del x-y del v/del y=y^2 v^k, then find k. If v(x,y))=(1-2xy+y^2)^(-1/2) and x ∂v/∂x-y ∂v/∂y=y^2 v^k,then find k. Question Question If v(x,y))=(1-2xy+y^2)^(-1/2) and x del v/del x-y del v/del y=y^2 v^k, then find k. If v(x,y))=(1-2xy+y^2)^(-1/2) and x ∂v/∂x-y ∂v/∂y=y^2 v^k,then find k. Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that  x…

If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x del u/del x+y del u/del y+z del u/del z If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x ∂u/∂x+y ∂u/∂y+z ∂u/∂z Question Question If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x del u/del x+y del u/del y+z del u/del z If u=sin^(-1)((x+2y+3z)/(x^8+y^8+z^8)) then find x ∂u/∂x+y ∂u/∂y+z ∂u/∂z Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that  x ∂u/∂x+y ∂u/∂y=5/2…

State Euler’s theorem and use it to find, x del u/del x+y del u/del y when u=tan^(-1) ((x^2+y^2)/(x+y)) State Euler's theorem and use it to find, x∂u/∂x+y∂u/∂y when u=tan^(-1)((x^2+y^2)/(x+y)) Question Question State Euler’s theorem and use it to find, x del u/del x+y del u/del y when u=tan^(-1) ((x^2+y^2)/(x+y)) State Euler's theorem and use it to find, x∂u/∂x+y∂u/∂y when u=tan^(-1)((x^2+y^2)/(x+y)) Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del…

If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3) +y^(1/3) )), Show that x.del u/del x+y.del u/del y=(-1)/6.tan u If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3)+y^(1/3) )),Show that x.∂u/∂x+y.∂u/∂y=(-1)/6 tan⁡u Question Question If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3) +y^(1/3) )), Show that x.del u/del x+y.del u/del y=(-1)/6.tan u If u=cosec^(-1) ((x^(1/2)+y^(1/2))/(x^(1/3)+y^(1/3) )),Show that x.∂u/∂x+y.∂u/∂y=(-1)/6 tan⁡u Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that  x ∂u/∂x+y ∂u/∂y=5/2 u If u=√(x^4+y^4) tan^-1(y/x),…

if u=sin^(-1)((x^2+y^2)/(x+y)), Show that x del u/del x+y del u/del y=tan u If u=sin^(-1)⁡((x^2+y^2)/(x+y)), Show that x ∂u/∂x+y ∂u/∂y=tan u Question Question if u=sin^(-1)((x^2+y^2)/(x+y)), Show that x del u/del x+y del u/del y=tan u If u=sin^(-1)⁡((x^2+y^2)/(x+y)), Show that x ∂u/∂x+y ∂u/∂y=tan u Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y = 5/2 uprove that  x ∂u/∂x+y ∂u/∂y=5/2 u If u=√(x^4+y^4) tan^-1(y/x),…

If u=tan^(-1)((x^3+y^3)/(x+y)), Show that 1. x u_x+y u_y = sin2u 2. x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u If u=tan^(-1)⁡((x^3+y^3)/(x+y)), Show that 1.xu_x+yu_y=sin2u 2.x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u using Euler’s theorem Question Question If u=tan^(-1)((x^3+y^3)/(x+y)), Show that 1. x u_x+y u_y = sin2u 2. x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u If u=tan^(-1)⁡((x^3+y^3)/(x+y)), Show that 1.xu_x+yu_y=sin2u 2.x^2 u_xx+2x_y u_xy+y^2 u_yy=sin4u-sin2u Euler’s theorem Problems If u=(x^3+y^3)/sqrt(x+y) prove that x du/dx + y du/dy = 5/2 uIf u=(x^3+y^3)/sqrt(x+y) prove that x del u/del x + y del u/del y…