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Beliebt Rechnen >

taylor 10sqrt(1+x)

Lösung

taylor

10 1 + x

Lösung

10 + 5 x - \frac{5}{4} x^{2} + \frac{5}{8} x^{3} - \frac{25}{64} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 10 + \frac{\frac{d}{d x} ( 10 1 + x ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 10 1 + x ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 10 1 + x ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 10 + \frac{5}{1 !} x + \frac{- \frac{5}{2}}{2 !} x^{2} + \frac{\frac{15}{4}}{3 !} x^{3} + \frac{- \frac{75}{8}}{4 !} x^{4} + \dots

Fasse zusammen

= 10 + 5 x - \frac{5}{4} x^{2} + \frac{5}{8} x^{3} - \frac{25}{64} x^{4} + \dots

Beliebte Beispiele

integral of 1/(x^2(1-x))

\int \frac{1}{x ^{2} ( 1 - x )} d x

(\partial)/(\partial t)(e^{-7t}cos(pix))

\frac{\partial}{\partial t} (e^{- 7 t} cos (π x))

limit as x approaches pi/4 of (sin(x-pi/4))/(4x-pi)

x \to \frac{π}{4} lim (\frac{sin ( x - \frac{π}{4} )}{4 x - π})

x^{^{'}} + x = 0

1/x (dy)/(dx)= 1/(x^2+1)

\frac{1}{x} \frac{d y}{d x} = \frac{1}{x ^{2} + 1}