Clarification: Problem 3.10d
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CM
Oct 7, 2017, 3:54:12 PM10/7/17
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I'm not completely sure what E3.10d is asking for. Are we supposed to make use of part c somehow?
Jay Wang
Oct 7, 2017, 4:49:23 PM10/7/17
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It's unrelated to part (c). One way to approach this is to assume W(x)=W(0) + W'(0) x + W''(0) x^2/2.
We know W(0)=0, so by differentiating both sides of W exp(W) = x, one also finds W'(0)=1 (or rewrite the hint at the end as W' = exp(-W)/(1+W).
Similarly, one can differentiate again to obtain W''(0).
We know W(0)=0, so by differentiating both sides of W exp(W) = x, one also finds W'(0)=1 (or rewrite the hint at the end as W' = exp(-W)/(1+W).
Similarly, one can differentiate again to obtain W''(0).
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