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g-1-x-x-g-n-x-g-n-1-x-x-f-x-lim-n-g-n-x-Is-f-x-analytical-for-some-subset-of-R-




Question Number 4312 by prakash jain last updated on 08/Jan/16
g_1 (x)=x  g_n (x)=[g_(nāˆ’1) (x)]^x   f(x)=lim_(nā†’āˆž) g_n (x)  Is f(x) analytical for some subset of R?
$${g}_{\mathrm{1}} \left({x}\right)={x} \\ $$$${g}_{{n}} \left({x}\right)=\left[{g}_{{n}āˆ’\mathrm{1}} \left({x}\right)\right]^{{x}} \\ $$$${f}\left({x}\right)=\underset{{n}\rightarrow\infty} {\mathrm{lim}}{g}_{{n}} \left({x}\right) \\ $$$$\mathrm{Is}\:{f}\left({x}\right)\:\mathrm{analytical}\:\mathrm{for}\:\mathrm{some}\:\mathrm{subset}\:\mathrm{of}\:\mathbb{R}? \\ $$

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