taylor sqrt(1+x),1

Lösung

taylor

1 + x, 1

2 + \frac{1}{2 2} (x - 1) - \frac{1}{16 2} (x - 1)^{2} + \frac{1}{64 2} (x - 1)^{3} - \frac{5}{1024 2} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{\frac{1}{2 2}}{1 !} (x - 1) + \frac{- \frac{1}{8 2}}{2 !} (x - 1)^{2} + \frac{\frac{3}{32 2}}{3 !} (x - 1)^{3} + \frac{- \frac{15}{128 2}}{4 !} (x - 1)^{4} + \dots

Fasse zusammen

= 2 + \frac{1}{2 2} (x - 1) - \frac{1}{16 2} (x - 1)^{2} + \frac{1}{64 2} (x - 1)^{3} - \frac{5}{1024 2} (x - 1)^{4} + \dots

y^{^{'}} + 0.2 \cdot y = 5

d er i v a t i v e f (x) = x^{\frac{1}{6}}

\int x (x^{2} + 2) d x

\int t 4 + 9 t^{2} d t

\int \frac{1}{1 + 64 x ^{2}} d x