26: The squeeze should go

For the sake of completeness, the fact that x/2^x tends to zero should be proved, but that is a textbook example for the l'Hospital rule. Note that it was just proved that the power 2^x2 is even higher on the scale of powers than x^x.

What still remains is to put the "−1" in somehow. Note that comparison does not help here, since x^x/(2^x2 − 1) is larger than x^x/2^x2. The fact that a smaller term goes to zero means nothing for the larger one, it can go anywhere (well, anywhere in the positive area, including infinity and DNE). This is a nice example of a comparison that does not allow any conclusion. What to do?

Try the usual trick, factoring out the leading terms. You just worked out how the leading terms compare, so there should be no trouble.

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