taylor \sqrt[4]{x}

Lösung

taylor

4 x

1 + \frac{1}{4} (x - 1) - \frac{3}{32} (x - 1)^{2} + \frac{7}{128} (x - 1)^{3} - \frac{77}{2048} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{4}}{1 !} (x - 1) + \frac{- \frac{3}{16}}{2 !} (x - 1)^{2} + \frac{\frac{21}{64}}{3 !} (x - 1)^{3} + \frac{- \frac{231}{256}}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 1 + \frac{1}{4} (x - 1) - \frac{3}{32} (x - 1)^{2} + \frac{7}{128} (x - 1)^{3} - \frac{77}{2048} (x - 1)^{4} + \dots

\int 3 + s (s + 1)^{2} d s

d er i v a t i v e f (x) = ln (25 sin^{2} (x))

d er i v a t i v e y (X) = 0.167 X

x \to 0 lim (x^{9 s i n (x)})

x \to 4 + lim (\frac{3 x}{x - 4})