MATH 222 Midterm: MATH222 Fall 2010 Exam

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Instructions: total number of points: 100, no books, calculators or notes are allowed for the exam. Do not rip pages from the examination book: there are 4 versions of this examination. This exam comprises 7 pages, including this cover. 1 (c) 3a b, (d) 3b a, (e) 5b a. (a) has sum 1/2, (b) has sum 1/3, (c) has sum 2/3, (d) diverges to , (e) diverges to : the p-series. Represents the function (a) ex, (b) sin x, (c) cos x, (d) arctan x, (e) tan x. 4!9 (d) x + (e) x + x3. 5: at the point (2, 1) the direction in which the function f (x, y) = change is given by the vector x2. + y2 has the maximum rate of (a) i 2j, (b) i + 2j, (c) 2i + j, (d) i + 2j, (e) i 2j. + z2 = 3 of the function f (x, y, z) = x2 + y2.