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For questions 1-4, consider the surface \(S: z = \sqrt{1 - x^2 - y^2}\), where \(x^2 + y^2 \leq 1\).

1.  What shape is the surface \(S\)?

a.  A cone

b.  A paraboloid

c.  A plane

d.  A sphere

e.  A hemisphere

You should be able to do questions 2, 3, and 4 without actually computing the integrals, just by looking at the shape of the surface \(S\) and the given vector field.

2.  Is \(\int\int_S \langle 1, 0, 0\rangle \cdot \vec{N} dA\)?

a.  Positive

b.  Negative

c.  0

3.  Is \(\int\int_S \langle 0, 0, 1\rangle \cdot \vec{N} dA\)?

a.  Positive

b.  Negative

c.  0

4.  Is \(\int\int_S \langle 0, 0, -1\rangle \cdot \vec{N} dA\)?

a.  Positive

b.  Negative

c.  0