taylor x^{11/2},5

Lösung

taylor

x^{\frac{11}{2}}, 5

3125 \cdot 5^{\frac{1}{2}} + \frac{6875 \cdot 5 ^{\frac{1}{2}}}{2} (x - 5) + \frac{12375 \cdot 5 ^{\frac{1}{2}}}{8} (x - 5)^{2} + \frac{5775 \cdot 5 ^{\frac{1}{2}}}{16} (x - 5)^{3} + \frac{5775 \cdot 5 ^{\frac{1}{2}}}{128} (x - 5)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 3125 \cdot 5^{\frac{1}{2}} + \frac{\frac{d}{d x} ( x ^{\frac{11}{2}} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{11}{2}} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{11}{2}} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

Evaluate Derivatives

= 3125 \cdot 5^{\frac{1}{2}} + \frac{\frac{6875 \cdot 5 ^{\frac{1}{2}}}{2}}{1 !} (x - 5) + \frac{\frac{12375 \cdot 5 ^{\frac{1}{2}}}{4}}{2 !} (x - 5)^{2} + \frac{\frac{17325 \cdot 5 ^{\frac{1}{2}}}{8}}{3 !} (x - 5)^{3} + \frac{\frac{17325 \cdot 5 ^{\frac{1}{2}}}{16}}{4 !} (x - 5)^{4} + \dots

Fasse zusammen

= 3125 \cdot 5^{\frac{1}{2}} + \frac{6875 \cdot 5 ^{\frac{1}{2}}}{2} (x - 5) + \frac{12375 \cdot 5 ^{\frac{1}{2}}}{8} (x - 5)^{2} + \frac{5775 \cdot 5 ^{\frac{1}{2}}}{16} (x - 5)^{3} + \frac{5775 \cdot 5 ^{\frac{1}{2}}}{128} (x - 5)^{4} + \dots

\frac{d}{d x} (5 x^{2} e^{3 x - 7})

\frac{d y}{d x} + \frac{3}{x} y = 16 y^{3}

\int_{4}^{7} \frac{x}{x ^{2} + 6 x + 13} d x

t an g e n t f (x) = 2 x^{2} + 2 x, at x = - 3

\int x e - x d x