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Problem 7.8

12 November, 2015 - 11:22

Expand (1+x)^{1/3} in a Taylor series around x = 0. The value x= 28 lies outside this series’ radius of convergence, but we can nevertheless use it to extract the cube root of 28 by recognizing that 28^{1/3}=3(28/27)^{1/3}. Calculate the root to four significant figures of precision, and check it in the obvious way.