Rrj Rx

Current density in a cylindrical wire of radius R is given as J = {J0 (xR 1) & for & 0 ≤ x < R2 J0 xR & for & R2≤ x ≤ R The current flowing in the wire is.

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(e) R is re exive, symmetric, and transitive Thus R is an equivalence relation Example 2 Which of these relations on the set of all functions on Z !Z are equivalence relations?. Txt 1919 hdrsgml 1919 accession number conformed submission type 8k public document count 29 conformed period of report 1919 item information regulation fd disclosure item information financial statements and exhibits filed as of date 1919 date as. Therefore, we have shown that (fg)(x h) (fg)(x) = (f(x)g0(x) g(x)f0(x))h r fg(h) (19) where jr fg(h)j jhj!0 as h!0Therefore, by the Landau de nition of di erentiability, we have shown that fgis di erentiable at every point x2Uand that its derivative is equal to f(x)g0(x)g(x)f0(x) = fDg gDf.

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D ϊ P Q ځi V ` v Z R ` R j d ϊ P P ( Ҍ ` D R ` V j v Z R i Ԑ ` v Z R ` x ` ` o R ` Ԑ j D R i x ` R ` R ` ` x j. # cut here # This is a shell archive Remove anything before this line, # then unpack it by saving it in a file and typing "sh file". 3 p(x)Rx=fp(x)f(x)jf(x)2Rxgis an ideal of Rx for any commutative ring R with 1 4 In Zx, the set I = ff(x) 2 Zx j f(0) 0 (mod n)g is an ideal for any n 2inZ This generalizes an example on page 136 where n =2 5 For R = C(R;R), x any r 2 R The set I = ff 2 R j f(r)=0gis an ideal Note that it does not work to use a number other.

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