Find the Maclaurin series of

$\displaystyle f(x)=(1+x^2)^(2/3)$

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- Mar 29th 2010, 09:14 AMmathguy123Series Help!
Find the Maclaurin series of

$\displaystyle f(x)=(1+x^2)^(2/3)$ - Mar 29th 2010, 11:40 AMHallsofIvy
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.