taylor x^3,\at 16/3

Lösung

taylor

x^{3}, at \frac{16}{3}

\frac{3 ( at \frac{16}{3} ) ^{2}}{1 !} (x - at \frac{16}{3}) + \frac{6 at \frac{16}{3}}{2 !} (x - at \frac{16}{3})^{2} + (x - at \frac{16}{3})^{3}

Schritte zur Lösung

Apply the Taylor Formula

= (at \frac{16}{3})^{3} + \frac{\frac{d}{d x} ( x ^{3} ) ( at \frac{16}{3} )}{1 !} (x - at \frac{16}{3}) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{3} ) ( at \frac{16}{3} )}{2 !} (x - at \frac{16}{3})^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{3} ) ( at \frac{16}{3} )}{3 !} (x - at \frac{16}{3})^{3} + \dots

Evaluate Derivatives

= (at \frac{16}{3})^{3} + \frac{3 ( at \frac{16}{3} ) ^{2}}{1 !} (x - at \frac{16}{3}) + \frac{6 at \frac{16}{3}}{2 !} (x - at \frac{16}{3})^{2} + \frac{6}{3 !} (x - at \frac{16}{3})^{3} + \frac{0}{4 !} (x - at \frac{16}{3})^{4} + \frac{0}{5 !} (x - at \frac{16}{3})^{5} + \frac{0}{6 !} (x - at \frac{16}{3})^{6} + \frac{0}{7 !} (x - at \frac{16}{3})^{7} + \frac{0}{8 !} (x - at \frac{16}{3})^{8} + \frac{0}{9 !} (x - at \frac{16}{3})^{9} + \frac{0}{10 !} (x - at \frac{16}{3})^{10}

Fasse zusammen

= \frac{3 ( at \frac{16}{3} ) ^{2}}{1 !} (x - at \frac{16}{3}) + \frac{6 at \frac{16}{3}}{2 !} (x - at \frac{16}{3})^{2} + (x - at \frac{16}{3})^{3}

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (1) = 0, y^{^{'}} (1) = 8

d er i v a t i v e - cot (x)

y^{^{''''}} + 2 y^{^{''}} = 0

\int \frac{x + 2}{x ^{2} + 4 x} d x

\int \frac{1}{1 + 3 x} d x