taylor sin(x) pi/4

Lösung

taylor

sin (x) \frac{π}{4}

\frac{π}{4} x - \frac{π}{24} x^{3} + \frac{π}{480} x^{5} - \frac{π}{20160} x^{7} + \frac{π}{1451520} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( sin ( x ) \frac{π}{4} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( sin ( x ) \frac{π}{4} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( sin ( x ) \frac{π}{4} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

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

Fasse zusammen

= \frac{π}{4} x - \frac{π}{24} x^{3} + \frac{π}{480} x^{5} - \frac{π}{20160} x^{7} + \frac{π}{1451520} x^{9} + \dots

\int sec^{2} (11 x) d x

l a pl a ce t r an s f or m e^{- 9 t}

t an g e n t y = 3 + 6 x + 8 x e^{x}

\frac{d}{d x} (\frac{x ^{2}}{5 ( 1 - x )})

t a y l or x^{0.5}