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

The limit as x approaches 27 of (3-\sqrt[3]{x})/(27-x) is 1/27

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

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

\frac{1}{27}

Decimal

0.03703 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 27

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

Simplify

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

= \frac{1}{27}

f (x) = (9 - 6 x)^{2}, (1, 9)

\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})

What is the limit as x approaches 27 of (3-\sqrt[3]{x})/(27-x) ?
The limit as x approaches 27 of (3-\sqrt[3]{x})/(27-x) is 1/27