MATH 2E Study Guide - Midterm Guide: Signal-To-Interference-Plus-Noise Ratio, Cross Product, Multiple Integral
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Problem 1 : (a) use green"s theorem to evaluate(cid:82) (cid:68) 2x2ye x2 from (0, 0) to (1, 1) to (1, 0) to (0, 0), and f is the vector eld given by. C f dr, where c is the triangle. Let d be the domain inside the triangle c. D = {(x, y)|0 x 1, 0 yx}. 0 t , and the segment ( 1, 0) (1, 0). (cid:90) . = 2 cos4 t sin t dt = (cid:90) 1. 1 x 0 dx (cid:29) (cid:104) cos5 t cos3 t (2 sin t cos t) dt + (cid:105) (cid:28) 1 + xz (1 + xz)2 + 2z. Problem 2 : (a) let f(x, y, z) = are positive. (i) find divf. divf = 2x2y (1 + xz)3 + 2 = 2 + 2y(x2 + z2) (1 + xy)3 (ii) show that f is conservative. curlf =
