MATH 21A Midterm: MATH 21A Harvard 21a Fall 13Practice4
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Tth 11:30 francesco cavazzani: start by printing your name in the above box and check your section in the box to the left, do not detach pages from this exam packet or unstaple the packet, please write neatly. Answers which are illeg- ible for the grader cannot be given credit: show your work. Mark for each of the 20 questions the correct letter. The surface x2 + y2 + z2 + 2z = 0 is a sphere. The length of the vector h1, 2, 2i is an integer. The vector h3, 4i appears as a velocity vector of the curve ~r(t) = hcos(5t), sin(5t)i. namely, there is a t such that ~r (t) = h3, 4i. If ~t is the unit tangent vector, ~n is the unit normal vector, and ~b is the binormal vector, then ~b ~n = ~t .
