What is the limit as x approaches 0 of (\sqrt[3]{27x^3-2x+5})/(3x-1) ?

The limit as x approaches 0 of (\sqrt[3]{27x^3-2x+5})/(3x-1) is -\sqrt[3]{5}

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limit as x approaches 0 of (\sqrt[3]{27x^3-2x+5})/(3x-1)

x \to 0 lim (\frac{3 27 x ^{3} - 2 x + 5}{3 x - 1})

- 35

Decimal

- 1.70997 \dots

Solution steps

x \to 0 lim (\frac{3 27 x ^{3} - 2 x + 5}{3 x - 1})

Plug in the value

x = 0

= \frac{3 27 \cdot 0 ^{3} - 2 \cdot 0 + 5}{3 \cdot 0 - 1}

Simplify

\frac{3 27 \cdot 0 ^{3} - 2 \cdot 0 + 5}{3 \cdot 0 - 1} : - 35

= - 35

x \to \infty lim (\frac{2}{x} + 3)

x \to \infty lim ((1 + a x)^{\frac{b}{x}})

x \to - 1 lim (\frac{f ( x ) g ( x )}{3})

x \to \infty lim (18)

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

What is the limit as x approaches 0 of (\sqrt[3]{27x^3-2x+5})/(3x-1) ?
The limit as x approaches 0 of (\sqrt[3]{27x^3-2x+5})/(3x-1) is -\sqrt[3]{5}