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Unformatted text preview: f ( x ) by f ( x ) = xe cos(1 /x ) for x 6 = 0 . How should I deﬁne f (0) to make f continuous? 4. Deﬁne the function f ( x ) by f ( x ) = cos( x ) if x < 0, ax + b if 0 ≤ x ≤ 2, x 3 if 2 < x . What should the constants a and b be so that f ( x ) is continuous for all x ? 5. (Challenge problem) Deﬁne f ( x ) by f ( x ) = ( 1 if x is rational, if x is irrational. At which points is f ( x ) continuous? 2...
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
- Fall '09