taylor cos(x+1)

Lösung

taylor

cos (x + 1)

cos (1) - sin (1) x - \frac{cos ( 1 )}{2} x^{2} + \frac{sin ( 1 )}{6} x^{3} + \frac{cos ( 1 )}{24} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= cos (1) + \frac{- sin ( 1 )}{1 !} x + \frac{- cos ( 1 )}{2 !} x^{2} + \frac{sin ( 1 )}{3 !} x^{3} + \frac{cos ( 1 )}{4 !} x^{4} + \dots

Fasse zusammen

= cos (1) - sin (1) x - \frac{cos ( 1 )}{2} x^{2} + \frac{sin ( 1 )}{6} x^{3} + \frac{cos ( 1 )}{24} x^{4} + \dots

\frac{\partial}{\partial x} (12 y^{5} x^{3} + 35 y^{8} x^{6})

6 (t + 1) \frac{d y}{d t} - 5 y = 5 t

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

\frac{d}{d x} (x^{4} + y^{4} + z^{4} - 4 x y z)

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