123. (a) The binomial theorem (Appendix E) allows us to write kxkxx xkxk1128348223+=++++FHGIKJ≈+bg"for x±1. Thus, the end result from the solution of Problem 35-75 yields rRmmRmmm=+FHGIKJλλλ11214and mmmm+FHGIKJ113234λfor very large values of m. Subtracting these, we obtain ∆rmmRm=−=341412λ.(b) We take the differential of the area: dA = d(πr2) = 2πr dr, and replace drwith ∆rin anticipation of using the result from part (a). Thus, the area between adjacent rings for
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