Find the Maclaurin series of $\displaystyle f(x)=(1+x^2)^(2/3)$
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f(0)= 1 $\displaystyle f'(x)= (2/3)(x^2+ 1)^{1/3}(2x)= (4/3)x(x^2+ 1)^{1/3}$ so f'(0)= 0. $\displaystyle f"(x)= (4/3)(x^2+ 1)^{1/3}+ (8/9)x^2(x^+ 1)^{-2/3}$ so f"(0)= 4/3. Keep going until you see a pattern.
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