Engineering Answers

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.

State Newton s law of cooling. If the temperature of the air is 30^{0}C and thetemperature of the body drops from 80°C to 60^{0}C in 10 minutes. What will beits temperature after 20 minutes?

Solve the initial value problem y^{2}y -y^{3}tanx=sinxcos^{2}x,y(0)=1?

Solve (x^{2}D^{2}+4xD+2)y=(logx/x)^{2}|x>0 , where D=d/dx?