taylor xcos((pix)/2)

Lösung

taylor

x cos (\frac{π x}{2})

x - \frac{π ^{2}}{8} x^{3} + \frac{π ^{4}}{384} x^{5} - \frac{π ^{6}}{46080} x^{7} + \frac{π ^{8}}{10321920} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- \frac{3 π ^{2}}{4}}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{\frac{5 π ^{4}}{16}}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- \frac{7 π ^{6}}{64}}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{\frac{9 π ^{8}}{256}}{9 !} x^{9} + \dots

Fasse zusammen

= x - \frac{π ^{2}}{8} x^{3} + \frac{π ^{4}}{384} x^{5} - \frac{π ^{6}}{46080} x^{7} + \frac{π ^{8}}{10321920} x^{9} + \dots

t a y l or e^{- \frac{x ^{2}}{2}}

\frac{\partial}{\partial x} (e^{3 x} cos (2 y))

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

\int e^{X} d X

\frac{d y}{d x} y = tan (x^{2} - 4 x)