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Unformatted text preview: f ( x ) is continuous at x = a . (7%) (b) Suppose f ( x ) = sin ax bx , x > , 3 , x = , a 2 x + a + b , x < . If f is continuous for all x ∈ R , what are the values of a and b ? 6. (8%) (i) Let f ( x ) = x 3 + x3. Find an integer n such that f ( x ) contains a root on the interval [ n , n + 1 ] . Justify your answer. 1 (8%) (ii) Find the least upper bound of the set S = { x 6∈ Q  x 2 ≤ 16 } . You may use any results from your lectures or problem sets to prove your answer is correct. (7%) 7. Suppose f ( x ) is even and g ( x ) = lim t → t f ( x )f ( x2003 t ) exists for all x . Determine whether g ( x ) is even, odd, or neither. 2...
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This note was uploaded on 04/09/2010 for the course MAT 137 taught by Professor Uppal during the Spring '08 term at University of Toronto.
 Spring '08
 UPPAL
 Calculus

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