Limit of x^(1/lnx) as x approaches infinity

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In this video we find the limit of of (tanx/x)^1/x^2 as x approaches 0 using L'Hopitals rule. Each step is explained carefully. Limit Laws are taken for granted in this problem.

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Limit of x^x^x as x goes to 0+ :

Limit of (1+1/x)^x as x approaches infinity :

Limit of (x/x+a)^x as x approaches infinity :

Limit of x^x as x goes to 0+ :

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It's not only the limit that is equal to e, x^(1/ln(x)) is constant.

youian
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0:29 but condition to be x in ]0+; +∞[

ayoubouaadoud