limit as x approaches 0 of 3/x+3/(x^2-x)

解答

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

- 3

求解步骤

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

乘以

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

的共轭根式

: \frac{\frac{9}{x ^{2}} - \frac{9}{x ^{4} - 2 x ^{3} + x ^{2}}}{\frac{3}{x} - \frac{3}{x ^{2} - x}}

= x \to 0 lim (\frac{\frac{9}{x ^{2}} - \frac{9}{x ^{4} - 2 x ^{3} + x ^{2}}}{\frac{3}{x} - \frac{3}{x ^{2} - x}})

化简

\frac{\frac{9}{x ^{2}} - \frac{9}{x ^{4} - 2 x ^{3} + x ^{2}}}{\frac{3}{x} - \frac{3}{x ^{2} - x}} : \frac{3}{x - 1}

= x \to 0 lim (\frac{3}{x - 1})

代入值

x = 0

= \frac{3}{0 - 1}

化简

= - 3

\frac{d}{d x} (2 x + sin (x))

\frac{d}{d x} (\frac{x ^{2} cos ( x )}{tan ( x )})

\int (z + 1) e^{z} d z

x \to 0 + lim (\frac{2}{x} - \frac{1}{ln ( x )})

\int_{1}^{\infty} e^{- 2 x} d x