taylor x^{9/6},2

Lösung

taylor

x^{\frac{9}{6}}, 2

2 \cdot 2^{\frac{1}{2}} + \frac{3}{2 ^{\frac{1}{2}}} (x - 2) + \frac{3}{8 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{2} - \frac{1}{32 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{3} + \frac{3}{512 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 2 \cdot 2^{\frac{1}{2}} + \frac{\frac{d}{d x} ( x ^{\frac{9}{6}} ) ( 2 )}{1 !} (x - 2) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{9}{6}} ) ( 2 )}{2 !} (x - 2)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{9}{6}} ) ( 2 )}{3 !} (x - 2)^{3} + \dots

Evaluate Derivatives

= 2 \cdot 2^{\frac{1}{2}} + \frac{\frac{3}{2 ^{\frac{1}{2}}}}{1 !} (x - 2) + \frac{\frac{3}{4 \cdot 2 ^{\frac{1}{2}}}}{2 !} (x - 2)^{2} + \frac{- \frac{3}{16 \cdot 2 ^{\frac{1}{2}}}}{3 !} (x - 2)^{3} + \frac{\frac{9}{64 \cdot 2 ^{\frac{1}{2}}}}{4 !} (x - 2)^{4} + \dots

Fasse zusammen

= 2 \cdot 2^{\frac{1}{2}} + \frac{3}{2 ^{\frac{1}{2}}} (x - 2) + \frac{3}{8 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{2} - \frac{1}{32 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{3} + \frac{3}{512 \cdot 2 ^{\frac{1}{2}}} (x - 2)^{4} + \dots

n = 0 \sum \infty \frac{1}{sin ( n )}

y^{^{'}} = 3 y

x \to 1 lim (\frac{( 26 - x - 5 )}{17 - x - 4})

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{3 t}

\int - 2 e^{c o s (x)} sin (x) d x