Solutions to Old Final 1Matthew LeingangDecember 19, 2011True/False.1. Directional derivativeDuf= 1forf=hx,0,0iandu=h1,-1,1i.
2. Normal vector toz=x2+y2at(x, y, z) = (1,1,2)ish2,2,-1i.
3. In spherical coordinates the equationϕ=π/3describes a plane.
4. When the vector functionF, curveCand surfaceSsatisfy the hypothesesof Stokes’s theorem, the theorem concludes thatRCF·dr=RRS∇ ×FdS
5. An irrotational vector fieldFis one for which∇ ×F=0.1