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Solution For x 6˘0, jxj is a differentiable function with derivative sgn(x) ˘1 if x ¨0 ¡1 if x ˙0 Thus by the chain rule in the ﬁrst line and by the product rule in the second line, f 0(x) ˘3jxj2 sgn(x) ˘3xjxj f 00(x) ˘3jxj¯3x sgn(x) ˘3jxj¯3jxj˘6jxj Checking the cases for x ˘0 by hand, we have f 0(0) ˘ lim h!0 f (x¯h)¡ f (x) h ˘ lim. Û N ?,Å Â ê Á Ã èý?, ê é Å Ü ý e Õ !. Chapter 1 Measure on a ¾Algebra of Sets 1 Limits of sequences of sets Deﬂnition 1 Let (An)n2Nbe a sequence of subsets of a set X (a) We say that (An) is increasing if An ‰ An1 for all n 2 N, and decreasing if An ¾ An1 for all n 2 N (b) For an increasing sequence (An), we deﬂne lim n!1 An= 1n=1 An For a decreasing sequence (An), we deﬂne lim.

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Provided the sum converges Here p(x j)=P(X= x j) In terms of these moments, the mean „and variance ¾2 of Xare given simply by „ = „ 1;. ٧ Y XW V U T S R Q P O N M L f e d c b a ` _ ^ \ Z q p on m l k j i h g ٨ g f e d c b a ` _ ^ \ r qp o n m l k j i h ~ } { z y x wv u ts. ÿ€ € € ž€ z€Æ‹ Å À Š P ƒ P ` À ‚ ° Ð ‚ ð Ð 0 ` p € €` à @ 0 0 ` ‚ ð p Ð ð Author swhite eBook 1 þþþ H H $ €@Ã ÂdÁ À@ÌÌÀ@ÌÌÀ@ÌÌ®ÌÌ €ÌÌ€ÌÌ€ÌÌ€ff€@ qÊøÊøÊøÿ€ ÿ ÿÿ€ ÿ ÿÿ€ ÿ ÿ Á ÿÿö Êøÿ ÿÿ ÿÿ ÿÿ ÿ€ ™ d q €ó Footnote TableFootnote * à * à \t \t / Ð Ñ ;,É!?.

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ALLEN COUNTY BAR ASSOCIATION PRESENTS _ HOW TO STAY_ OUTi OF HOT_ WATER INN THE1 WORKPLACEAND_ WHATA HAPPENSt WHEN YOU_ DON’T Tp 3m hours CLE W Wednesday, December 18,0 13_ 10 pm ‐ 345 pm Allen County Bar Association.