MATH 201 Midterm: MATH 201 Exam 2
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This test is closed book and closed notes. For full credit show all of your work (legibly!). Each problem is worth 10 points (a total of 50 points): given two real numbers x and y we de ne. Prove that max{x, y} = (cid:26) x y if x y if x < y max{x, y} = x + |x y| + y. Since we have an expression involving an absolute value, i. e. , |x y|, we will proceed by cases. First, suppose that x y, so that x y 0 and |x y| = x y. In this case we have that max{x, y} = x while x + |x y| + y. 2 x + x y + y. Second, suppose that x < y, so that x y < 0 and |x y| = (x y) = y x. In this case we have that max{x, y} = y while x + |x y| + y.
