taylor arcsin(x),0

Lösung

taylor

arcsin (x), 0

x + \frac{1}{6} x^{3} + \frac{3}{40} x^{5} + \frac{5}{112} x^{7} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{1}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{9}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{225}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \dots

Fasse zusammen

= x + \frac{1}{6} x^{3} + \frac{3}{40} x^{5} + \frac{5}{112} x^{7} + \dots

\int (6 x^{2}) (e^{x^{3} + 2}) d x

d er i v a t i v e 9 cos (x)

a re a y = - x^{2} + 16, y = 0, x = - 2, x = 3

\frac{d y}{d x} = - \frac{3 x ^{2} + 2 y ^{2}}{4 x y}

\frac{d y}{d x} = 9 x