taylor (-5x+24)^{3/2}

Lösung

taylor

(- 5 x + 24)^{\frac{3}{2}}

48 \cdot 6^{\frac{1}{2}} - 15 \cdot 6^{\frac{1}{2}} x + \frac{25 \cdot 3 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}} x^{2} + \frac{125}{768 \cdot 6 ^{\frac{1}{2}}} x^{3} + \frac{625}{49152 \cdot 6 ^{\frac{1}{2}}} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 48 \cdot 6^{\frac{1}{2}} + \frac{\frac{d}{d x} ( ( - 5 x + 24 ) ^{\frac{3}{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( - 5 x + 24 ) ^{\frac{3}{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( - 5 x + 24 ) ^{\frac{3}{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 48 \cdot 6^{\frac{1}{2}} + \frac{- 15 \cdot 6 ^{\frac{1}{2}}}{1 !} x + \frac{\frac{25 \cdot 3 ^{\frac{1}{2}}}{8 \cdot 2 ^{\frac{1}{2}}}}{2 !} x^{2} + \frac{\frac{125}{128 \cdot 6 ^{\frac{1}{2}}}}{3 !} x^{3} + \frac{\frac{625}{2048 \cdot 6 ^{\frac{1}{2}}}}{4 !} x^{4} + \dots

Fasse zusammen

= 48 \cdot 6^{\frac{1}{2}} - 15 \cdot 6^{\frac{1}{2}} x + \frac{25 \cdot 3 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}} x^{2} + \frac{125}{768 \cdot 6 ^{\frac{1}{2}}} x^{3} + \frac{625}{49152 \cdot 6 ^{\frac{1}{2}}} x^{4} + \dots

a re a f (x) = 4 - (x - 1)^{2}, (1, 3)

\int \frac{r ^{3}}{4 - r ^{2}} d r

\int \frac{x}{x ^{4} + 4} d x

\frac{d}{d x} (tan (\frac{x}{5}))

\frac{d}{d x} ((11 - 3 x)^{\frac{2}{3}} (x - 2)^{4})