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Popular >

taylor cos(x), pi/3

Solution

taylor

cos (x), \frac{π}{3}

Solution

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

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