taylor x^{9/6},7

Lösung

taylor

x^{\frac{9}{6}}, 7

7 \cdot 7^{\frac{1}{2}} + \frac{3 \cdot 7 ^{\frac{1}{2}}}{2} (x - 7) + \frac{3}{8 \cdot 7 ^{\frac{1}{2}}} (x - 7)^{2} - \frac{1}{112 \cdot 7 ^{\frac{1}{2}}} (x - 7)^{3} + \frac{3}{6272 \cdot 7 ^{\frac{1}{2}}} (x - 7)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 7 \cdot 7^{\frac{1}{2}} + \frac{\frac{d}{d x} ( x ^{\frac{9}{6}} ) ( 7 )}{1 !} (x - 7) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{9}{6}} ) ( 7 )}{2 !} (x - 7)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{9}{6}} ) ( 7 )}{3 !} (x - 7)^{3} + \dots

Evaluate Derivatives

= 7 \cdot 7^{\frac{1}{2}} + \frac{\frac{3 \cdot 7 ^{\frac{1}{2}}}{2}}{1 !} (x - 7) + \frac{\frac{3}{4 \cdot 7 ^{\frac{1}{2}}}}{2 !} (x - 7)^{2} + \frac{- \frac{3}{56 \cdot 7 ^{\frac{1}{2}}}}{3 !} (x - 7)^{3} + \frac{\frac{9}{784 \cdot 7 ^{\frac{1}{2}}}}{4 !} (x - 7)^{4} + \dots

Fasse zusammen

= 7 \cdot 7^{\frac{1}{2}} + \frac{3 \cdot 7 ^{\frac{1}{2}}}{2} (x - 7) + \frac{3}{8 \cdot 7 ^{\frac{1}{2}}} (x - 7)^{2} - \frac{1}{112 \cdot 7 ^{\frac{1}{2}}} (x - 7)^{3} + \frac{3}{6272 \cdot 7 ^{\frac{1}{2}}} (x - 7)^{4} + \dots

\int - 2 e^{- 3 c o s (3 x)} sin (3 x) d x

\frac{\partial}{\partial x} (e^{p (x)} (p (x) + p (x) p (x)))

\int e^{a x + b} d x

\frac{d}{d t} (7 cos^{3} (t))

\int (4 cos^{2} (x)) d x