I need to prove whether the given expression is finite but not infinitesimal/infinite/infinitesimal.$$H-K\over H^2 + K^2$$ Where ##H, K## are +ve infinite numbers.(adsbygoogle = window.adsbygoogle || []).push({});

I did the following,

Let ##H = \alpha K, \alpha \in R##

then,

$${\alpha K-K\over \alpha^2K^2 + K^2} \implies {\alpha - 1\over K(\alpha^2 + 1)}$$

Since ##{\alpha - 1\over (\alpha^2 + 1)}## is finite and ##K##, infinite. Thus the given expression is infinitesimal.

I am not sure if this is correct.

Am I correct ?

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# I Can I do this for hyperreals?

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