limit as x approaches 27 of (3-\sqrt[3]{x})/(27-x)

解答

x \to 27 lim (\frac{3 - 3 x}{27 - x})

\frac{1}{27}

十进制

0.03703 \dots

求解步骤

x \to 27 lim (\frac{3 - 3 x}{27 - x})

使用洛必达法则

= x \to 27 lim (\frac{- \frac{1}{3 x ^{\frac{2}{3}}}}{- 1})

代入值

x = 27

= \frac{- \frac{1}{3 \cdot 2 7 ^{\frac{2}{3}}}}{- 1}

化简

\frac{- \frac{1}{3 \cdot 2 7 ^{\frac{2}{3}}}}{- 1} : \frac{1}{27}

= \frac{1}{27}

t an g e n t f (x) = (9 - 6 x)^{2}, (1, 9)

in v erse l a pl a ce \frac{1}{s ^{2} ( 1 + 7 s )}

\frac{d}{d x} (x (1 - \frac{x}{10}))

\frac{d}{d x} (5 x cos (x^{2}))

x \to + 0 lim (\frac{5}{x ^{2} + x} - \frac{5}{x})