maclaurin sin(3x+2)

Lösung

maclaurin

sin (3 x + 2)

sin (2) + 3 cos (2) x - \frac{9 sin ( 2 )}{2} x^{2} - \frac{9 cos ( 2 )}{2} x^{3} + \frac{27 sin ( 2 )}{8} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= sin (2) + \frac{3 cos ( 2 )}{1 !} x + \frac{- 9 sin ( 2 )}{2 !} x^{2} + \frac{- 27 cos ( 2 )}{3 !} x^{3} + \frac{81 sin ( 2 )}{4 !} x^{4} + \dots

Fasse zusammen

= sin (2) + 3 cos (2) x - \frac{9 sin ( 2 )}{2} x^{2} - \frac{9 cos ( 2 )}{2} x^{3} + \frac{27 sin ( 2 )}{8} x^{4} + \dots

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

\frac{d}{d x} (- 0.4 x^{2} + 1000)

\frac{\partial}{\partial y} (x y - 3 x z + yz)

\int \frac{x ^{5}}{x ^{2} + 8} d x

x \to 3 lim (\frac{- x}{x - 3})