taylor x*sec(x)

Lösung

taylor

x \cdot sec (x)

x + \frac{1}{2} x^{3} + \frac{5}{24} x^{5} + \frac{61}{720} x^{7} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{25}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{427}{7 !} x^{7} + \dots

Fasse zusammen

= x + \frac{1}{2} x^{3} + \frac{5}{24} x^{5} + \frac{61}{720} x^{7} + \dots

\int \frac{1}{x 16 x ^{2} - 9} d x

\frac{\partial}{\partial x} (\frac{7}{x ^{3}})

\int (sin^{3} (x) cos (x)) d x

\int e^{- \frac{2 r}{a}} r^{2} d r

t an g e n t f (x) = x^{3}, at - 5