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Unformatted text preview: f is not Riemann integrable on [0 , 1] The function g dened by g ( x ) = sin f ( x ) is Riemann integrable on [0 , 1] Prove your claims using the denition of the Riemann integral. 6. Let f : R 3 R 3 be a mapping dened by y 1 = x 1 + x 2 y 2 = x 2-x 1 y 3 = x 5 3 (a) Determine all points a R 3 at which f satises the assumptions of the Inverse Func-tion Theorem. (b) Is f an open mapping? Prove or disprove. Reminder. A mapping f : R 3 R 3 is open if f ( W ) is an open subset of R 3 for every open set W R 3 ....
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This note was uploaded on 06/19/2011 for the course MATH 600 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.
- Spring '11