I am struggling with equations like those: $$\liminf(1/x)^{1/x}$$ $$\liminf(x)^{1/x}$$ But I am not able to solve them - I always get $$\infty^{0}\;\text{ or }\;0^{0}$$.
Can anybody give me a tip how to deal with stuff like that?
calculating limits that include ^(1/x)
0
$\begingroup$
analysis
limits
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0You take the log of it! – 2017-01-26
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0@KKJ I think it is better to come up with actual exercises you are struggling with, show some effort and share with us where you get stuck – 2017-01-26
1 Answers
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Hints:
$$(1/x)^{1/x}=e^{(1/x)\ln(1/x)}$$
$$x^{1/x}=e^{(1/x)\ln(x)}$$
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0but is not then $$1^{-infinity}$$ and $$1^{infinity}$$? It is the only way of transforming the equations I can see (besides coming back to their basic forms) – 2017-01-27
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0@KKJ my answer is to point out that you should tackle the problem as follows:$$\liminf (1/x)\ln(1/x)\\\liminf x\ln(1/x)$$ and then take e^ of each. – 2017-01-27