MATH 215 Midterm: exam1f10sol
Document Summary
On problems 4 and 5 you can get partial credit. Z 1 t2 dt = 2 t3 + c t ru e/f alse. False (b) d dx (3 arctan 5x) = False (c) the dot product of two vectors is always orthogonal to the plane through the two vectors. Dot product is a number, not a vector. False (d) the two expressions ~r1(t) = (cos t, sin t, t) and ~r2(t) = (cos(2t), sin(2t), 2t) parametrize the same helix. Replacing t by 2t reparametrizes the curve. true (e) 1 pt4 + 2 + 1/t4dt = z 2. 1 (f) the gradient of the unit normal vector to a surface is always tangent to the surface. The unit normal is a vector, not a function. 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.
