泰勒 f(x)=8.8sqrt(x)

解答

泰勒

f (x) = 8.8 x

8.8 + 4.4 (x - 1) - 1.1 (x - 1)^{2} + 0.55 (x - 1)^{3} - 0.34375 (x - 1)^{4} + \dots

求解步骤

应用泰勒公式

= 8.8 + \frac{\frac{d}{d x} ( 8.8 x ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( 8.8 x ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 8.8 x ) ( 1 )}{3 !} (x - 1)^{3} + \dots

求导数

= 8.8 + \frac{4.4}{1 !} (x - 1) + \frac{- 2.2}{2 !} (x - 1)^{2} + \frac{3.3}{3 !} (x - 1)^{3} + \frac{- 8.25}{4 !} (x - 1)^{4} + \dots

整理后得

= 8.8 + 4.4 (x - 1) - 1.1 (x - 1)^{2} + 0.55 (x - 1)^{3} - 0.34375 (x - 1)^{4} + \dots

\frac{d}{d x} (e^{2 x} x (a cos (x) + b sin (x)))

x \to 8 + lim (\frac{3}{x - 8})

\frac{d}{d x} (- \frac{x ^{2}}{2})

d er i v a t i v e 2 5 x^{3}

t an g e n t f (x) = \frac{- 8 x}{x ^{2} + 1}, at x = 0