泰勒 sqrt(10-x),1

解答

泰勒

10 - x, 1

3 - \frac{1}{6} (x - 1) - \frac{1}{216} (x - 1)^{2} - \frac{1}{3888} (x - 1)^{3} - \frac{5}{279936} (x - 1)^{4} + \dots

求解步骤

应用泰勒公式

= 3 + \frac{\frac{d}{d x} ( 10 - x ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( 10 - x ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 10 - x ) ( 1 )}{3 !} (x - 1)^{3} + \dots

求导数

= 3 + \frac{- \frac{1}{6}}{1 !} (x - 1) + \frac{- \frac{1}{108}}{2 !} (x - 1)^{2} + \frac{- \frac{1}{648}}{3 !} (x - 1)^{3} + \frac{- \frac{5}{11664}}{4 !} (x - 1)^{4} + \dots

整理后得

= 3 - \frac{1}{6} (x - 1) - \frac{1}{216} (x - 1)^{2} - \frac{1}{3888} (x - 1)^{3} - \frac{5}{279936} (x - 1)^{4} + \dots

x \to - \infty lim (x^{4})

t an g e n t f (x) = 4 x^{3} + 3 x, at x = - 4, - 1

y^{^{'}} + \frac{y}{t} = 6 cos (5 t)

\int x^{2} (x^{3} + 8)^{11} d x

x \to 0 lim (2 x^{2} - 3)