ch35-p123 - 123. (a) The binomial theorem (Appendix E)...

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123. (a) The binomial theorem (Appendix E) allows us to write kx k xx x k x k 11 28 3 48 2 23 += + + + + F H G I K J ≈+ bg " for x ± 1. Thus, the end result from the solution of Problem 35-75 yields rR m m Rm m m =+ F H G I K J λλ λ 1 1 2 1 4 and m m m m + F H G I K J 1 1 3 2 3 4 λ for very large values of m . Subtracting these, we obtain r m m R m =−= 3 4 1 4 1 2 λ . (b) We take the differential of the area: dA = d ( π r 2 ) = 2 π r dr , and replace dr with r in anticipation of using the result from part (a). Thus, the area between adjacent rings for
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