MATH 21A Study Guide - Final Guide: Talking Lifestyle 1278, Multiple Integral, Ellipse
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Answers which are illegible for the grader cannot be given credit: show your work. Except for problems 1-3, we need to see details of your computation: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 180 minutes time to complete your work. Mark for each of the 20 questions the correct letter. The length of the curve ~r(t) = hsin(t), t4 + t, cos(t)i on t [0, 1] is the same as the length of the curve ~r(t) = hsin(t2), t8 + t2, cos(t2)i on [0, 1]. The parametric surface ~r(u, v) = (5u 3v, u v 1, 5u v 7) is a plane. Any function u(x, y) that obeys the di erential equation uxx + ux uy = 1 has no local maxima. The length of the vector projection of ~b onto a vector ~a is smaller or equal than the length of the vector ~b.
