Question
Find the limit. \( \lim _{x \rightarrow 0} \frac{1}{x^{2 / 3}} \)
Ask by Hill Watkins. in Malaysia
Mar 14,2025
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Answer
The limit is \( +\infty \).
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As \( x \) approaches 0 from the positive side, \( \frac{1}{x^{2/3}} \) tends towards positive infinity because the denominator becomes extremely small, causing the whole fraction to blow up. Conversely, as \( x \) approaches 0 from the negative side, the expression also trends toward positive infinity. Therefore, we can conclude that: \[ \lim _{x \rightarrow 0} \frac{1}{x^{2 / 3}} = +\infty \]