Question: In this problem, letSbe the surface defined be the equations:x2+y2+z2= 1,x2+y21/2, andz0. (a) (1 point) Find a parametrization ofS :DR3 whereDR2(Hint: use spherical coordinates). (b)(2

In this problem, letSbe the surface defined be the equations:x2+y2+z2= 1,x2+y21/2, andz0.

(a) (1 point) Find a parametrization ofS

:DR3

whereDR2(Hint: use spherical coordinates).

(b)(2 points) Use part (a) to find the area ofS.

(c)(1 point) LetF:R3R3be the vector fieldF(x,y,z) = (y,x,ln(x2+y2+1)).

Compute F.

(d)(3 points) LetFbe the vector field from part (c). Use Stokes' theorem to evaluate

(F)dA

where is the parametrization from part (a).

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