6. (20%) Find the first four nonzero terms in the Maclaurin series for (a) $\frac{1}{\sqrt{1-t^2}}$, and
(b) $\sin^{-1}x = \int_0^x \frac{1}{\sqrt{1-t^2}} \, dt$.
阿摩線上測驗
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阿摩線上測驗
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6. (20%) Find the first four nonzero terms in the Maclaurin series for (a) $\frac{1}{\sqrt{1-t^2}}$, and
(b) $\sin^{-1}x = \int_0^x \frac{1}{\sqrt{1-t^2}} \, dt$.