taylor cos(x-7x)

Lösung

taylor

cos (x - 7 x)

1 - 18 x^{2} + 54 x^{4} - \frac{324}{5} x^{6} + \frac{1458}{35} x^{8} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( cos ( x - 7 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( cos ( x - 7 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( cos ( x - 7 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{- 36}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{1296}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 46656}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{1679616}{8 !} x^{8} + \dots

Fasse zusammen

= 1 - 18 x^{2} + 54 x^{4} - \frac{324}{5} x^{6} + \frac{1458}{35} x^{8} + \dots

n = 0 \sum \infty 6^{n} x^{n}

n = 1 \sum \infty \frac{4}{n}

\int \frac{3}{2 x - 1} d x

d y - k y d x = 0

\int \frac{1}{4 u ^{2} + 23} d u