泰勒 7/(sqrt(x)),4

解答

泰勒

\frac{7}{x}, 4

\frac{7}{2} - \frac{7}{16} (x - 4) + \frac{21}{256} (x - 4)^{2} - \frac{35}{2048} (x - 4)^{3} + \frac{245}{65536} (x - 4)^{4} + \dots

求解步骤

应用泰勒公式

= \frac{7}{2} + \frac{\frac{d}{d x} ( \frac{7}{x} ) ( 4 )}{1 !} (x - 4) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{7}{x} ) ( 4 )}{2 !} (x - 4)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{7}{x} ) ( 4 )}{3 !} (x - 4)^{3} + \dots

求导数

= \frac{7}{2} + \frac{- \frac{7}{16}}{1 !} (x - 4) + \frac{\frac{21}{128}}{2 !} (x - 4)^{2} + \frac{- \frac{105}{1024}}{3 !} (x - 4)^{3} + \frac{\frac{735}{8192}}{4 !} (x - 4)^{4} + \dots

整理后得

= \frac{7}{2} - \frac{7}{16} (x - 4) + \frac{21}{256} (x - 4)^{2} - \frac{35}{2048} (x - 4)^{3} + \frac{245}{65536} (x - 4)^{4} + \dots

\int_{1}^{4} x ln (\frac{x}{2}) d x

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = 0

\int_{- 5}^{1} (2 x + 6) d x

d er i v a t i v e \frac{7}{t}

l a pl a ce t r an s f or m \frac{1}{2} t^{2}