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Evaluate: ("lim")(xtooo)x^(1/x)...

Evaluate: `("lim")_(xtooo)x^(1/x)`

Text Solution

Verified by Experts

We have `y=underset(xtooo)limx^((1)/(x))" "(oo^(0))`
`:." "logy=log_(e)(underset(xtooo)limx^((1)/(x)))`
`=underset(xtooo)lim(log_(e)x^((1)/(x)))`
`=underset(xtooo)lim(log_(e)x)/(x)" "((oo)/(oo)"form")`
`=underset(xtooo)lim(1//x)/(1)" "`(Using L'Hospital Rule)
`=0`
`:." "y=1`
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