taylor sqrt(x)4

Lösung

taylor

x 4

4 + 2 (x - 1) - \frac{1}{2} (x - 1)^{2} + \frac{1}{4} (x - 1)^{3} - \frac{5}{32} (x - 1)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

= 4 + 2 (x - 1) - \frac{1}{2} (x - 1)^{2} + \frac{1}{4} (x - 1)^{3} - \frac{5}{32} (x - 1)^{4} + \dots

f^{^{'}} (x) = 1.9181 \cdot x^{2} + 177.69 \cdot x - 0.4 \cdot x^{3}

d er i v a t i v e (8 - 9 x) (8 + 9 x)

d er i v a t i v e (1 - \frac{x}{2})^{e^{x^{2}}}

n = 1 \sum \infty \frac{4}{n ^{3}}

y^{^{''}} + 36 y = - 2 tan (6 x)