taylor 5/(sqrt(x)),4

Lösung

taylor

\frac{5}{x}, 4

\frac{5}{2} - \frac{5}{16} (x - 4) + \frac{15}{256} (x - 4)^{2} - \frac{25}{2048} (x - 4)^{3} + \frac{175}{65536} (x - 4)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{5}{2} + \frac{\frac{d}{d x} ( \frac{5}{x} ) ( 4 )}{1 !} (x - 4) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{5}{x} ) ( 4 )}{2 !} (x - 4)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{5}{x} ) ( 4 )}{3 !} (x - 4)^{3} + \dots

Evaluate Derivatives

= \frac{5}{2} + \frac{- \frac{5}{16}}{1 !} (x - 4) + \frac{\frac{15}{128}}{2 !} (x - 4)^{2} + \frac{- \frac{75}{1024}}{3 !} (x - 4)^{3} + \frac{\frac{525}{8192}}{4 !} (x - 4)^{4} + \dots

Fasse zusammen

= \frac{5}{2} - \frac{5}{16} (x - 4) + \frac{15}{256} (x - 4)^{2} - \frac{25}{2048} (x - 4)^{3} + \frac{175}{65536} (x - 4)^{4} + \dots

n = 0 \sum \infty \frac{1}{e ^{5 n}}

\int (- 4 x^{3} + 2 e^{- 2 x} + \frac{1}{2 x}) d x

\frac{d y}{d x} + 4 (tan (4 x)) y = 10 cos (4 x)

x \to 0 lim (\frac{x}{( 4 ^{x} - 2 ^{x} )})

\frac{d}{d x} (arcsin (2 x^{5}))