泰勒 xe^{x^3}

解答

泰勒

x e^{x^{3}}

x + x^{4} + \frac{1}{2} x^{7} + \frac{1}{6} x^{10} + \dots

求解步骤

应用泰勒公式

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

求导数

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{2520}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{604800}{10 !} x^{10} + \dots

整理后得

= x + x^{4} + \frac{1}{2} x^{7} + \frac{1}{6} x^{10} + \dots

\int \frac{1}{0.15 p + 20} d p

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t an g e n t g (x) = - x^{2} + 4 x^{2} - 2 x + 2