10. Represent $f(x) = \ln(8 - x^3)$ as a power series. Find the interval of convergence for the power series.
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To find the power series representation of ln(8-3x), we can use the Taylor series expansion of ln(1+x), where x = -3x/8. ln(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ... Substituting x = -3x/8, we have: ln(8-3x) = (-3x/8) - ((-3x/8)^2)/2 + ((-3x/8)^3)/3 - Show more…
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