MATH 251, Section Quiz 3 (Sections 11.6, 11.7, 12.1). Dr. M. Vorobets

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MATH 251, Section
Thursday, Sept. 19, 2013
Quiz 3 (Sections 11.6, 11.7, 12.1).
Dr. M. Vorobets
NAME (print):
No credit for unsupported answers will be given. Calculators can be used for simple
arithmetic operations only! Clearly indicate your final answer
1. [3 pts.] Find ⃗r(t) if ⃗r ′ (t) = t2⃗ı + cos(t)⃗ȷ − tet⃗k and ⃗r(0) = ⃗ı − 2⃗ȷ + ⃗k.
2. [4 pts.] Find the curvature of the curve ⃗r(t) =< 1 + t, 1 − t, 3t2 >.
[more problems on back]
3. [3 pts.] Sketch the domain of the function
√
f (x, y) = x2 + y 2 − 1 + ln(4 − x2 − y 2 )
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