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Find the following limits:lim(xrarr1)x^(...

Find the following limits:`lim_(xrarr1)x^(1/(1-x)`

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Let `y=`lim_(xrarr1)x^(1/(1-x) implies ln y=(lnx)/(1-x)`
`implies ln y=(lnx)/(1-x) ` (0/0 form)
`=lim_(xrarr1)1/(-x)=-1implies lim_(xrarr1)y=e^(-1)`
`therefore lim_(xrarr1)x^(1/(1-x))=1/e`
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MBD PUBLICATION-APPLICATION OF DERIVATIVES-QUESTION BANK
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