Why is limit of this function infinity as x approaches infinity

functionslimits

I typed this function into symbolab and I got the next answer:
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Why is the limit of the function as x approaches infinity even possible to calculate if we get beyond the domain of the function? How does this online calculator process $\sqrt{-∞}$?

Best Answer

The online calculator is correct if you regard the complex plane as being completed by a single point $\infty$, but is wrong if you view $\infty$ as being a set of complex numbers with phase (as Mathematica does, for example).

The most unambiguous way to express the answer is probably "infinity, approached along the positive imaginary axis".

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