Chemical Engineering Answers

b) Find the complete integral of the PDE px + qy +z = xq^2?

State Green s theorem and verify for *(x^{2}+y^{2})dx+(3y+2x)dy ,whereC is triangle with vertices at (0,0),(1,0),(1,1)

Evaluate the line integral of ∀ =xyl+ y^{2}zj+e^{2z}k over the curve C whoseparametric representation is given by x=t^{2},y=2t,z=t,0<t<1

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.