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Unformatted text preview: . 4 4. (a) [1 mark] Formulate The Monotone Sequence Theorem (b) [5 marks] Show that exists and find its value if is defined k k x + lim } { k x recursively by 1 = x and 2 1 2 1 1 + = + k k x x 5 5. (a) [2 marks] Let denote the line segment in R i L 2 from the origin (0, 0) to the point ) 1 , 1 ( 2 i i , ( i = 1, 2, 3, . .) on the curve . Is the union 2 ) ( x x f = S = compact? Justify your answer. i i L = 1 U (b) [4 marks] Suppose S R n is compact, f : S R is continuous, and f ( x ) > 1 for every x S . Show that there is a number c > 1 such that f ( x ) c for every x S . 6...
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This note was uploaded on 10/21/2010 for the course MATHEMATIC MAT237Y1 taught by Professor Romauldstanczak during the Fall '09 term at University of Toronto Toronto.
 Fall '09
 RomauldStanczak
 Calculus

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