taylor e^{-x},1

Lösung

taylor

e^{- x}, 1

\frac{1}{e} - \frac{1}{e} (x - 1) + \frac{1}{2 e} (x - 1)^{2} - \frac{1}{6 e} (x - 1)^{3} + \frac{1}{24 e} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{e} + \frac{- \frac{1}{e}}{1 !} (x - 1) + \frac{\frac{1}{e}}{2 !} (x - 1)^{2} + \frac{- \frac{1}{e}}{3 !} (x - 1)^{3} + \frac{\frac{1}{e}}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= \frac{1}{e} - \frac{1}{e} (x - 1) + \frac{1}{2 e} (x - 1)^{2} - \frac{1}{6 e} (x - 1)^{3} + \frac{1}{24 e} (x - 1)^{4} + \dots

\frac{\partial}{\partial x} ((cos (x))^{2})

t an g e n t - \frac{1}{( x - 6 ) ^{2}}

\int csc (4 x) d x

\frac{d}{d x} (arcsinh (x))

\frac{d}{d t} (3 t (t^{2} + 4))