泰勒 e^{-x},-0.75

解答

泰勒

e^{- x}, - 0.75

2.11700 \dots - 2.11700 \dots (x + 0.75) + 1.05850 \dots (x + 0.75)^{2} - 0.35283 \dots (x + 0.75)^{3} + 0.08820 \dots (x + 0.75)^{4} + \dots

求解步骤

应用泰勒公式

= 2.11700 \dots + \frac{\frac{d}{d x} ( e ^{- x} ) ( - 0.75 )}{1 !} (x + 0.75) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{- x} ) ( - 0.75 )}{2 !} (x + 0.75)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{- x} ) ( - 0.75 )}{3 !} (x + 0.75)^{3} + \dots

求导数

= 2.11700 \dots + \frac{- 2.11700 \dots}{1 !} (x + 0.75) + \frac{2.11700 \dots}{2 !} (x + 0.75)^{2} + \frac{- 2.11700 \dots}{3 !} (x + 0.75)^{3} + \frac{2.11700 \dots}{4 !} (x + 0.75)^{4} + \dots

整理后得

= 2.11700 \dots - 2.11700 \dots (x + 0.75) + 1.05850 \dots (x + 0.75)^{2} - 0.35283 \dots (x + 0.75)^{3} + 0.08820 \dots (x + 0.75)^{4} + \dots

f^{^{''}} (x) = x

in v erse l a pl a ce \frac{s - 2}{s ^{2} - 4 s + 5}

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

\int \frac{- 2000 x}{25 - x ^{2}} d x

\frac{d}{d x} (ln (arcsin (x)))