泰勒 7+6sin(x^2)

解答

泰勒

7 + 6 sin (x^{2})

7 + 6 x^{2} - x^{6} + \frac{1}{20} x^{10} + \dots

求解步骤

应用泰勒公式

= 7 + \frac{\frac{d}{d x} ( 7 + 6 sin ( x ^{2} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 7 + 6 sin ( x ^{2} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 7 + 6 sin ( x ^{2} ) ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 7 + \frac{0}{1 !} x + \frac{12}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{181440}{10 !} x^{10} + \dots

整理后得

= 7 + 6 x^{2} - x^{6} + \frac{1}{20} x^{10} + \dots

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