taylor 5sin^2(x)

Lösung

taylor

5 sin^{2} (x)

5 x^{2} - \frac{5}{3} x^{4} + \frac{2}{9} x^{6} - \frac{1}{63} x^{8} + \frac{2}{2835} x^{10} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 5 sin ^{2} ( x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 5 sin ^{2} ( x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 5 sin ^{2} ( x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{10}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 40}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{160}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 640}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{2560}{10 !} x^{10} + \dots

Fasse zusammen

= 5 x^{2} - \frac{5}{3} x^{4} + \frac{2}{9} x^{6} - \frac{1}{63} x^{8} + \frac{2}{2835} x^{10} + \dots

d er i v a t i v e y = (6 x - 5)^{2} (3 - x^{5})^{2}

x \to - 1 lim (x^{3} + 1)

x \to 0 lim (\frac{1 - cos ( 8 x )}{4 x ^{2}})

\frac{\partial}{\partial x} (8 x^{9 y})

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