limit as z approaches 2 of ((2z-z^2)/(z^2-4))^3

解答

z \to 2 lim ((\frac{2 z - z ^{2}}{z ^{2} - 4})^{3})

- \frac{1}{8}

十进制

- 0.125

求解步骤

z \to 2 lim ((\frac{2 z - z ^{2}}{z ^{2} - 4})^{3})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

不定型除外

= (z \to 2 lim (\frac{2 z - z ^{2}}{z ^{2} - 4}))^{3}

化简

\frac{2 z - z ^{2}}{z ^{2} - 4} : - \frac{z}{z + 2}

= (z \to 2 lim (- \frac{z}{z + 2}))^{3}

代入值

z = 2

= (- \frac{2}{2 + 2})^{3}

化简

(- \frac{2}{2 + 2})^{3} : - \frac{1}{8}

= - \frac{1}{8}

x \to 1.5 lim (\frac{7 x ^{2} + 14 x - 21}{3 - 2 x})

x \to - 1 lim (5 x^{2} - 3 x - 2)

x \to 2 lim (5 x^{3} + 10 x)

x \to 20 lim (x^{2} - 3 x + 4)

x \to \frac{π}{2} lim (\frac{x}{tan ( x )})