MIT18_014F10_pset3

MIT18_014F10_pset3 - , 1] by our denition of integrability....

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Unit 3: Limits and Continuity - Week 1 Pset 3 Due September 30 (4 points each) (1) page 83:21 (2) page 94:10 (3) For step functions s ( x ) ,t ( x ) de±ned on [ a,b ] prove the Cauchy-Schwarz inequality: b b b ± ² 2 s ( x ) t ( x ) dx s ( x ) 2 dx · t ( x ) 2 dx. a a a Show that equality holds iff s ( x ) = ct ( x ) where c R . (4) Bonus: Let B = { x [0 , 1] x = m/ 2 n for some m,n Z } Prove that the function | ³ f ( x ) = 1 : x B 0 : x / B is not integrable on [0
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Unformatted text preview: , 1] by our denition of integrability. 1 MIT OpenCourseWare http://ocw.mit.edu 18.014 Calculus with Theory Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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This note was uploaded on 01/18/2012 for the course MATH 18.014 taught by Professor Christinebreiner during the Fall '10 term at MIT.

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MIT18_014F10_pset3 - , 1] by our denition of integrability....

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