maclaurin cos(pix)

Lösung

maclaurin

cos (π x)

1 - \frac{π ^{2}}{2} x^{2} + \frac{π ^{4}}{24} x^{4} - \frac{π ^{6}}{720} x^{6} + \frac{π ^{8}}{40320} x^{8} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 - \frac{π ^{2}}{2} x^{2} + \frac{π ^{4}}{24} x^{4} - \frac{π ^{6}}{720} x^{6} + \frac{π ^{8}}{40320} x^{8} + \dots

\frac{d y}{d x} + y cos (x) = 3 cos (x), y (0) = 5

a re a y = 4 x - x^{2}, y = x

\frac{d x}{d t} + 8 x = 0

\frac{d}{d x} (4 x (sin (x) + cos (x)))

\frac{d y}{d x} = \frac{x - 1}{y ^{3}}