deletions | additions       diff --git a/textbf_textit_Calculus_of_the__.tex b/textbf_textit_Calculus_of_the__.tex  index 773790a..b5f2e1d 100644  --- a/textbf_textit_Calculus_of_the__.tex  +++ b/textbf_textit_Calculus_of_the__.tex 
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-\frac{1}{2}\left(1-k\right)\left(1-4b+3k\right)  \end{array}\right).  \end{align*}  Rearranging, this yields  $$  s^{*}\left(b,k\right)=\left(b-\frac{1}{2}\right)+\frac{\left(1-k\right)^{2}}{2\left(b-k\right)+\left(1-k\right)^{2}}\left(\frac{1}{2}-2b+k+\frac{1}{3}b^{2}f\left(\frac{k}{b}\right)\right),