Question

Choose the correct answer with steps

1)Let c be a positive constant. The surface given in terms of spherical coordinates as {(ρ,θ,ϕ):0≤ρ≤c,0≤θ≤2π,0≤ϕ≤π/2} is a:

a. sphere that has −π as its absolute minimum value.

b. hemisphere that has c as its absolute maximum value.

c. hemisphere that has c as its absolute minimum value.

d. sphere that has cπ as its absolute minimum value.

2) Let F(x,y,z)=〈2xy+z,x²,x〉be a conservative vector field. A potential function of F is:

a. 〈2y,0,0〉

b. x²y+xz

c. xy+xz

d. 2y

e. x²y