化简 1/3 x^{3/2}-x^{1/2}

解答

化简

\frac{1}{3} x^{\frac{3}{2}} - x^{\frac{1}{2}}

\frac{x ^{\frac{3}{2}}}{3} - x^{\frac{1}{2}}

求解步骤

\frac{1}{3} x^{\frac{3}{2}} - x^{\frac{1}{2}}

使用分式法则:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

\frac{1}{3} x^{\frac{3}{2}} = \frac{1 \cdot x ^{\frac{3}{2}}}{3}

= \frac{1 \cdot x ^{\frac{3}{2}}}{3} - x^{\frac{1}{2}}

使用法则:

1 \cdot a = a

1 \cdot x^{\frac{3}{2}} = x^{\frac{3}{2}}

= \frac{x ^{\frac{3}{2}}}{3} - x^{\frac{1}{2}}

\int \frac{1}{x ^{3}} d x

f (x) = x^{\frac{1}{5}}

x \to 2 lim (5 x - 14 x^{- 2})

\int_{0}^{π} (1 - sin (x)) d x

x \to 13 lim (x - 4)