what is the coefficient of x^2 in the power series expansion of (4 + 7x)^(1/3)?

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- Feb 5th 2009, 04:31 PMmr_motivatorpower series expansion
what is the coefficient of x^2 in the power series expansion of (4 + 7x)^(1/3)?

- Feb 5th 2009, 04:41 PMbob murray
Try a Taylor expansion:

$\displaystyle f(x)=f(a)+(x-a)\frac{\partial}{\partial x} f(a) + \frac{(x-a)^{2}}{2!} \frac{\partial^{2}}{\partial x^{2}} f(a) + ...$

Use $\displaystyle a = 0$, and take the necessary derivatives. The third term in the above series is what you're looking for.