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Unformatted text preview: f ( x ) = π + cos 2 ( 1-e x ) , f ( ) = 1 . (5%) (a) Show that f has an inverse. (7%) (b) Find ( f-1 ) ( 1 ) . 1 5. (8%) (a) Find all continuous functions f ( t ) which satisfy Z x 2 f ( t ) dt = e 2 x 2-1; and verify your answer; otherwise show that such a function does not exist. (4%) (b) Does there exist a continuous function f which satisﬁes Z x f ( t ) dt = e x ? (10%) 6. Show for all real numbers x and y that if x 6 = y , then | tan-1 x-tan-1 y | < | x-y | . 2...
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- Spring '08
- Calculus, Continuous function, Toronto Term Test