Find the gradient ?f.f(x, y, z) = xy3ex + z
A. ex + z[(xy3 + y3)i + 3xy2j + k]
B. (xy3ex + y3)i + 3xy2ex + zj + ezk]
C. ex + z[(3xy2 + y3)i + 3xy2j + k]
D. (xy3ex + z + y3ex + z)i + 3xy2ex + zj + ezk]
Answer: A
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Find decimal notation.
A. 0.4
B. 0.4
C. 0.
D. 0.
Solve the problem.At noon, ship A was 14 nautical miles due north of ship B. Ship A was sailing south at 14 knots (nautical miles per hour; a nautical mile is 2000 yards) and continued to do so all day. Ship B was sailing east at 
and continued to do so all day. The visibility was 5 nautical miles. Did the ships ever sight each other?
A. Yes. They were within 3 nautical miles of each other. B. Yes. They were within 4 nautical miles of each other. C. No. The closest they ever got to each other was 6.3 nautical miles. D. No. The closest they ever got to each other was 7.3 nautical miles.
Evaluate the integral in terms of natural logarithms.
A. 7 ln (4 + 
)
B. 4
C. ln (4 + 
)
D. 7 ln (1 + 
)
Multiply using the rules for special products.(w - t)2
A. w2 - 2wt - t2 B. w2 - 2wt + t2 C. w2 + 2wt + t2 D. w2 - wt + t2