taylor 7tan(x)

Lösung

taylor

7 tan (x)

7 x + \frac{7}{3} x^{3} + \frac{14}{15} x^{5} + \frac{17}{45} x^{7} + \frac{62}{405} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 7 tan ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 7 tan ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 7 tan ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{7}{1 !} x + \frac{0}{2 !} x^{2} + \frac{14}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{112}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{1904}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{55552}{9 !} x^{9} + \dots

Fasse zusammen

= 7 x + \frac{7}{3} x^{3} + \frac{14}{15} x^{5} + \frac{17}{45} x^{7} + \frac{62}{405} x^{9} + \dots

\frac{d}{d x} (e x^{2} - y)

\int (x^{2} + 3)^{5} 2 x d x

\int 64 e^{8 x} sin (8 x) d x

\frac{\partial}{\partial x} (cos^{2} (x) + sin^{2} (y))

\int sin^{2} (t) d tan (t)