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Popular >

taylor sin(x), 1/6 pi

Solution

taylor

sin (x), \frac{1}{6} π

Solution

\frac{1}{2} + \frac{3}{2} (x - \frac{1}{6} π) - \frac{1}{4} (x - \frac{1}{6} π)^{2} - \frac{1}{4 3} (x - \frac{1}{6} π)^{3} + \frac{1}{48} (x - \frac{1}{6} π)^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( sin ( x ) ) ( \frac{1}{6} π )}{1 !} (x - \frac{1}{6} π) + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( x ) ) ( \frac{1}{6} π )}{2 !} (x - \frac{1}{6} π)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( x ) ) ( \frac{1}{6} π )}{3 !} (x - \frac{1}{6} π)^{3} + \dots

Evaluate Derivatives

= \frac{1}{2} + \frac{\frac{3}{2}}{1 !} (x - \frac{1}{6} π) + \frac{- \frac{1}{2}}{2 !} (x - \frac{1}{6} π)^{2} + \frac{- \frac{3}{2}}{3 !} (x - \frac{1}{6} π)^{3} + \frac{\frac{1}{2}}{4 !} (x - \frac{1}{6} π)^{4} + \dots

Refine

= \frac{1}{2} + \frac{3}{2} (x - \frac{1}{6} π) - \frac{1}{4} (x - \frac{1}{6} π)^{2} - \frac{1}{4 3} (x - \frac{1}{6} π)^{3} + \frac{1}{48} (x - \frac{1}{6} π)^{4} + \dots

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