http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx(adsbygoogle = window.adsbygoogle || []).push({});

According to the author, if ##c## is a real number and ##r## is a positive rational number then:

$$\lim_{x →\infty} \frac{c}{x^r} = 0$$

If ##x^r## is defined for ##x < 0## then:

$$\lim_{x →- \infty} \frac{c}{x^r} = 0$$

I understand why ##r## can't be irrational in case two. ##x^r## would not be defined.

However, I can't see why ##r## can't be irrational in case one.

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# Limits at infinity

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