taylor cos(x)

Lösung

taylor

cos (x)

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 1 - \frac{1}{2 !} x^{2} + \frac{1}{4 !} x^{4} - \frac{1}{6 !} x^{6} + \frac{1}{8 !} x^{8} + \dots

Die Reihensummen Darstellung

= n = 0 \sum \infty (- 1)^{n} \frac{x ^{2 n}}{( 2 n ) !}

x \to 0 lim (x^{2} - sin (\frac{1}{x}))

d er i v a t i v e y = x^{3} (2 x + 3)^{7}

a re a 3 x, \frac{3}{x}, x = 3

\frac{d y}{d x} = - \frac{y}{x}

x \to 0 lim (cos (π))