What is the limit as x approaches 0-of 2/3 x^{-1/3} ?

The limit as x approaches 0-of 2/3 x^{-1/3} is -infinity

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limit as x approaches 0-of 2/3 x^{-1/3}

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

- \infty

Solution steps

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

Simplify

\frac{2}{3} x^{- \frac{1}{3}} : \frac{2}{3 x ^{\frac{1}{3}}}

= x \to 0 - lim (\frac{2}{3 x ^{\frac{1}{3}}})

For

x

approaching

0

from the left

, x < 0 \Rightarrow 3 x^{\frac{1}{3}} < 0

The denominator is a negative quantity approaching 0 from the left

= - \infty

\int_{0}^{\infty} e^{- 14 x} d x

\frac{d ^{3}}{d x ^{3}} (\frac{1 - 5 x}{1 + 5 x})

x \to - 3 lim (14)

f (x) = x^{2} + 8, (2, 12)

\int 3 x^{\frac{2}{3}} d x

What is the limit as x approaches 0-of 2/3 x^{-1/3} ?
The limit as x approaches 0-of 2/3 x^{-1/3} is -infinity