MATH 2004 Midterm: Exam-MATH2004-2008December
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Part a: multiple choice questions (2 marks each) The area enclosed by one loop of the lemniscate r2 = sin 2 (0 . 2 ) is (a) (b) (c) (d) (e) 1. Suppose that the angle between the vectors u = i k and v = 2i + aj is (a) 3, (b) 3 (c) 3, (d) 2, (e) 3. The acceleration vector r (t) of r(t) = t3 i + (sin t)j at t = 1. Then fxx + fxy is equal to (a) 12x2y, (b) 3x2 + 2y, (c) x2 + y, (d) 6x2y + 6xy2, (e) 6xy + 3x2y. Suppose that the gradient of f (x, y) is given by f = yi + xj and suppose that w = f (s + t, s t). T (a) s2t, is equal to (b) s t, (c) 2t, (d) 2s, (e) s + t.
