taylor sin(x),3

Lösung

taylor

sin (x), 3

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

x \to 2 lim (4 x + 1)

\int \frac{1}{( 1 + x ^{2} ) ^{3}} d x

x \to - 3 lim (x^{2} + 7 x + 12)

\int \frac{x}{5 x ^{2} + 3} d x

\frac{d}{d x} (\frac{6 - sec ( x )}{tan ( x )})