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| Math Central | Quandaries & Queries |
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Question from Neil, a student: The limit of [(1/x)^3 - 1/8]^1/3 all over (x - 1/2) as x approaches 1/2 to positive infinity. How to answer that? |
Hi Neil,
This is a strange problem
\[\lim_{x \rightarrow \frac12} \frac{[\frac{1}{x}^3 - \frac18]^{1/3}}{x - \frac12}.\]
Are you sure that you have it stated properly?
If this is the correct problem then as $x$ approaches $\large \frac12$ the denominator approaches $0$ and the numerator approaches $[2^3 - \large \frac18]^{1/3}$ which is not zero and hence the limit approaches infinity.
Harley
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