taylor sqrt(x+3)

Lösung

taylor

x + 3

3 + \frac{1}{2 3} x - \frac{1}{24 3} x^{2} + \frac{1}{144 3} x^{3} - \frac{5}{3456 3} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 3 + \frac{\frac{1}{2 3}}{1 !} x + \frac{- \frac{1}{12 3}}{2 !} x^{2} + \frac{\frac{1}{24 3}}{3 !} x^{3} + \frac{- \frac{5}{144 3}}{4 !} x^{4} + \dots

Fasse zusammen

= 3 + \frac{1}{2 3} x - \frac{1}{24 3} x^{2} + \frac{1}{144 3} x^{3} - \frac{5}{3456 3} x^{4} + \dots

\frac{d}{d s} (\frac{3}{s ^{2} + 9})

cos^{2} (t) \frac{d y}{d t} = 1

\frac{d}{d x} (\frac{3 x - 1}{x})

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2})

\frac{d ^{2}}{d x ^{2}} (x^{2})