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MIT18_014F10_pset3

# MIT18_014F10_pset3 - 1 by our de±nition of integrability 1...

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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 ) defined on [ a, b ] prove the Cauchy-Schwarz inequality: b b b 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 | f ( x ) = 1 : x B 0 : x / B is not integrable

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Unformatted text preview: , 1] by our de±nition 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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