taylor cos(x+pi/2)

Lösung

taylor

cos (x + \frac{π}{2})

- x + \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( cos ( x + \frac{π}{2} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( x + \frac{π}{2} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( x + \frac{π}{2} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{- 1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{1}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 1}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{1}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 1}{9 !} x^{9} + \dots

Fasse zusammen

= - x + \frac{1}{6} x^{3} - \frac{1}{120} x^{5} + \frac{1}{5040} x^{7} - \frac{1}{362880} x^{9} + \dots

\int_{- 1}^{1} \frac{1}{2} (6 - 6 x^{2})^{2} d x

\int t (t + 1)^{6} d t

t an g e n t f (x) = x^{2} - 1, at x = 2

a re a y = e^{x}, y = e^{2 x}, x = 0, x = ln (2)

t an g e n t f (x) = 4 x^{2} - 4 x + 1, at x = 0