Unformatted text preview: • f is not Riemann integrable on [0 , 1] • The function g deﬁned by g ( x ) = sin f ( x ) is Riemann integrable on [0 , 1] Prove your claims using the deﬁnition of the Riemann integral. 6. Let f : R 3 → R 3 be a mapping deﬁned by y 1 = x 1 + x 2 y 2 = x 2x 1 y 3 = x 5 3 (a) Determine all points a ∈ R 3 at which f satisﬁes the assumptions of the Inverse Function 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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 Spring '11
 NA
 Topology, Sets, Continuous function, Metric space, Open set, Riemann

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