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Unformatted text preview: (8%) 4. Find d 2 dx 2 Z x Z sin t 1 e u 2 du dt . 5. Suppose f ( x ) = 2 x + cos x . (6%) (a) Show that f ( x ) is one-to-one. (6%) (b) Find ( f-1 ) ( 1 ) . 6. Suppose f is continuous on [ a , b ] . (8%) (a) Prove there exists c [ a , b ] such that Z c a f ( t ) dt = Z b c f ( t ) dt . (4%) (b) Must there exist c ( a , b ) such that Z c a f ( t ) dt = Z b c f ( t ) dt ? Justify your answer with an appropriate proof or counterexample. 1...
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This note was uploaded on 10/14/2010 for the course MAT MAT taught by Professor Unknown during the Spring '10 term at Touro CA.
- Spring '10