taylor (x+xcos(x)-2sin(x))/(x^3)

Lösung

taylor

\frac{x + x cos ( x ) - 2 sin ( x )}{x ^{3}}

1 + cos (1) - 2 sin (1) + (5 sin (1) - 4 cos (1) - 2) (x - 1) + \frac{17 cos ( 1 ) - 18 sin ( 1 ) + 6}{2} (x - 1)^{2} + \frac{85 sin ( 1 ) - 88 cos ( 1 ) - 24}{6} (x - 1)^{3} + \frac{541 cos ( 1 ) - 490 sin ( 1 ) + 120}{24} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + cos (1) - 2 sin (1) + \frac{\frac{d}{d x} ( \frac{x + x c o s ( x ) - 2 s i n ( x )}{x ^{3}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{x + x c o s ( x ) - 2 s i n ( x )}{x ^{3}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{x + x c o s ( x ) - 2 s i n ( x )}{x ^{3}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + cos (1) - 2 sin (1) + \frac{5 sin ( 1 ) - 4 cos ( 1 ) - 2}{1 !} (x - 1) + \frac{17 cos ( 1 ) - 18 sin ( 1 ) + 6}{2 !} (x - 1)^{2} + \frac{85 sin ( 1 ) - 88 cos ( 1 ) - 24}{3 !} (x - 1)^{3} + \frac{541 cos ( 1 ) - 490 sin ( 1 ) + 120}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 1 + cos (1) - 2 sin (1) + (5 sin (1) - 4 cos (1) - 2) (x - 1) + \frac{17 cos ( 1 ) - 18 sin ( 1 ) + 6}{2} (x - 1)^{2} + \frac{85 sin ( 1 ) - 88 cos ( 1 ) - 24}{6} (x - 1)^{3} + \frac{541 cos ( 1 ) - 490 sin ( 1 ) + 120}{24} (x - 1)^{4} + \dots

\frac{d}{d x} ((2 x - 5)^{4} (8 x^{2} - 5)^{- 3})

\frac{d}{d x} (2 x^{8})

d er i v a t i v e 21000 (0.92)^{13}

\int \frac{sec ^{2} ( x )}{tan ( x )} d x

d er i v a t i v e f (x) = x^{2} - 4 x + 3