Chemical Engineering Answers

The unit normal to the surface x² + y² + z² = 3 at (1,1,1) is. A)1/√16 (2i+2j+2k) B)1/√3(i+j+ k)

C) 1/√6(i+2j+3k)

D)1/√3(i+2j+2k)

If Ø(x, y, z) = x² - y²-2²-2, then ∇Ø at (2,1,-1) is ,,,choose the correct answer?

A) 4i +2j-2k

B)4i-2j-2k

C) 4i + 2j + 2k

D)4i - 2j +2k

Solve (x²D²-3xD+4)y=2x²

State Green s theorem and verify for ∮c(x²+y²)dx+(3y+2x)dy ,where C is triangle with vertices at (0,0),(1,0),(1,1)

Evaluate the line integral of →{v}=xyi+y^{2}zj+e^{2z}k over the curve C whose parametric representation is given by x=t^{2},y=2t,z=t,0<t<1.

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

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 dy/dx= 4x² (y-x)² + if y /x is a particular solution.

Solve (2y³xe^y+ y² + y)dx + (y³x²e^y-xy- 2x)dy = 0.