Power Serieseasy
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When using the first 3 terms of the Maclaurin series for sin(x)\sin(x) to approximate sin(0.2)\sin(0.2), what is the maximum error by the alternating series test?

Series: sin(x)=xx33!+x55!x77!+\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots

First 3 terms: P3(0.2)=0.2(0.2)36+(0.2)5120P_3(0.2) = 0.2 - \frac{(0.2)^3}{6} + \frac{(0.2)^5}{120}