taylor \sqrt[3]{x},27

Lösung

taylor

3 x, 27

3 + \frac{1}{27} (x - 27) - \frac{1}{2187} (x - 27)^{2} + \frac{5}{531441} (x - 27)^{3} - \frac{10}{43046721} (x - 27)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 3 + \frac{\frac{d}{d x} ( 3 x ) ( 27 )}{1 !} (x - 27) + \frac{\frac{d ^{2}}{d x ^{2}} ( 3 x ) ( 27 )}{2 !} (x - 27)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 3 x ) ( 27 )}{3 !} (x - 27)^{3} + \dots

Evaluate Derivatives

= 3 + \frac{\frac{1}{27}}{1 !} (x - 27) + \frac{- \frac{2}{2187}}{2 !} (x - 27)^{2} + \frac{\frac{10}{177147}}{3 !} (x - 27)^{3} + \frac{- \frac{80}{14348907}}{4 !} (x - 27)^{4} + \dots

Fasse zusammen

= 3 + \frac{1}{27} (x - 27) - \frac{1}{2187} (x - 27)^{2} + \frac{5}{531441} (x - 27)^{3} - \frac{10}{43046721} (x - 27)^{4} + \dots

in v erse l a pl a ce \frac{1}{( x ^{2} + 1 ) ^{2}}

\frac{\partial}{\partial y} (e^{x - 2 y})

\int_{0}^{1} x y d x

y^{^{''}} - (\frac{3}{x}) y^{^{'}} - (\frac{6}{x ^{2}}) y = 0

im pl i c i t ln (5 + e^{x y}) = y