taylor (sqrt(x))/2 ,4

Lösung

taylor

\frac{x}{2}, 4

1 + \frac{1}{8} (x - 4) - \frac{1}{128} (x - 4)^{2} + \frac{1}{1024} (x - 4)^{3} - \frac{5}{32768} (x - 4)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{8}}{1 !} (x - 4) + \frac{- \frac{1}{64}}{2 !} (x - 4)^{2} + \frac{\frac{3}{512}}{3 !} (x - 4)^{3} + \frac{- \frac{15}{4096}}{4 !} (x - 4)^{4} + \dots

Fasse zusammen

= 1 + \frac{1}{8} (x - 4) - \frac{1}{128} (x - 4)^{2} + \frac{1}{1024} (x - 4)^{3} - \frac{5}{32768} (x - 4)^{4} + \dots