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Evaluate lim(xto1^(+)) 2^(-2^((1)/(1-x))...

Evaluate `lim_(xto1^(+)) 2^(-2^((1)/(1-x))).`

Text Solution

Verified by Experts

`underset(xto1^(+))lim2^(-2^((1)/(1-x)))=underset(hto0)lim2^(-2^((1)/(1-(1+h))))=underset(hto0)lim2^(-2^((1)/(-h)))`
Now when `hrarr0,-1/hrarr-oo,`
`:." "2^(-1/h)rarr0^(-)`
`implies" "-2^(-1/h)rarr0^(+)`
`implies" "2^(-2^(1/-h))rarr1`
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