Chemical Engineering Answers

Show that curl(curl→{v})=grad(div→{v})-V^{2}→{v},→{v} is any vector and if isolenoidal, then find curl (curl ∀)

Find the angle between the surfaces x^{2}+y^{2}+z^{2}=9 and z+3=x^{2}+y^{2} at the point (-2,1,2)

Show that the vector →{v}=(yz-1)i-z(1+x+z)j+y(1+x+2z)k isconservative and find it scalar potential function?

Find the directional derivative of f(x,y,z)=xyz^{2}+xz along the tangentto the curve x=t,y=t^{2},z=t^{3} at the point (1,1,1)

Find the volume of the tetrahedron boulded by the coordinate planes and theplane x/a+y/b+z/c=1

Evaluate ∬R(x-y)^{2}sin^{2}(x+y)d xdy, where R is the rhombus withsuccessive vertices at (π,0),(2π,π),(π,2t) and (0,π)

Evaluate ∫y=0^{1}∫x=y^{2√2-y^{2}}y/2√x^{2}+y^{2}dxdy ,by clange the order of integration.

Solve (2y^{3}xe^{y}+y^{2}+y)dx+(y^{3}x^{2}y^{y}-xy-2x)dy=0

Solve dy/dx=4x^{2}(y-x)^{2}+y/x if y=x is a particular solution

Find the equation of the family of all erhogonal trajectories of the family ofcircles which pass through origin and hav centres on the y-axis.