MATH 215 Midterm: exam1f10
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On problems 4 and 5 you can get partial credit. Z 1 t2 dt = 2 t3 + c t ru e/f alse (b) d dx (3 arctan 5x) = T ru e/f alse (c) the dot product of two vectors is always orthogonal to the plane through the two vectors. True/false (d) the two expressions ~r1(t) = (cos t, sin t, t) and ~r2(t) = (cos(2t), sin(2t), 2t) parametrize the same helix. T ru e/f alse (f) the gradient of the unit normal vector to a surface is always tangent to the surface. Note: go over your calculations again to make sure you have the right expressions for ~ab, ~ac. You lose a lot of points if you get them wrong. What is the total distance travelled by the particle along the helix? (c) suppose z is de ned implicitly as a function of x, y by.