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taylor 7sin(x), pi/4

Solution

taylor

7 sin (x), \frac{π}{4}

Solution

\frac{7}{2} + \frac{7}{2} (x - \frac{π}{4}) - \frac{7}{2 2} (x - \frac{π}{4})^{2} - \frac{7}{6 2} (x - \frac{π}{4})^{3} + \frac{7}{24 2} (x - \frac{π}{4})^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{7}{2} + \frac{\frac{d}{d x} ( 7 sin ( x ) ) ( \frac{π}{4} )}{1 !} (x - \frac{π}{4}) + \frac{\frac{d ^{2}}{d x ^{2}} ( 7 sin ( x ) ) ( \frac{π}{4} )}{2 !} (x - \frac{π}{4})^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 7 sin ( x ) ) ( \frac{π}{4} )}{3 !} (x - \frac{π}{4})^{3} + \dots

Evaluate Derivatives

= \frac{7}{2} + \frac{\frac{7}{2}}{1 !} (x - \frac{π}{4}) + \frac{- \frac{7}{2}}{2 !} (x - \frac{π}{4})^{2} + \frac{- \frac{7}{2}}{3 !} (x - \frac{π}{4})^{3} + \frac{\frac{7}{2}}{4 !} (x - \frac{π}{4})^{4} + \dots

Refine

= \frac{7}{2} + \frac{7}{2} (x - \frac{π}{4}) - \frac{7}{2 2} (x - \frac{π}{4})^{2} - \frac{7}{6 2} (x - \frac{π}{4})^{3} + \frac{7}{24 2} (x - \frac{π}{4})^{4} + \dots

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