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In questions 1 and 2, consider the surface \(z^2 - x^2 - y^2 = 4\)

1.  An equation of the tangent plane to this surface at the point \((1, 2, 3)\) is

a.  \(-x - 2y + 3z = 8\)

b.  \(-x - 2y + 3z = 4 \)

c.  \( x + 2y + 3z = 14 \)

d.  \(-x + 2y - 3z = -6 \)

e.  \( x + 2y + 3z = -14 \)

2.  An equation of the normal line to this surface at the point \((1, 2, 3)\) is

a.  \(x = 1 - t, y = 2 - 2t, z = 3 + 3t \)

b.  \( x = 1 + t, y = 2 - 2t, z = 3 + 3t \)

c.  \( x = 1 - t, y = 2 + 2t, z = 3 + 3t \)

d.  \( x = 1 + t, y = 2 + 2t, z = 3 + 3t \)

e.  \( x = 1 - t, y = 2 - 2t, z = 3 - 3t \)

3.  Compute the directional derivative of the function \( f(x,y) = xe^y + x^3\) at the point \( (1, 0) \) in the direction given by vector \( {\bf v} = \langle 3, 4 \rangle \).

a.  \( \sqrt(17) \)

b.  \( 3 \)

c.  \( 16 \)

d.  \( \frac{16}{5} \)

e.  \( 0 \)