maclaurin arctan(5x)

Lösung

maclaurin

arctan (5 x)

5 x - \frac{125}{3} x^{3} + 625 x^{5} - \frac{78125}{7} x^{7} + \frac{1953125}{9} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( arctan ( 5 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( arctan ( 5 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( arctan ( 5 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{5}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 250}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{75000}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 56250000}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{78750000000}{9 !} x^{9} + \dots

Fasse zusammen

= 5 x - \frac{125}{3} x^{3} + 625 x^{5} - \frac{78125}{7} x^{7} + \frac{1953125}{9} x^{9} + \dots