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Evaluate lim(xto1) (x^(2)+xlog(e)x-log(e...

Evaluate `lim_(xto1) (x^(2)+xlog_(e)x-log_(e)x-1)/((x^(2))-1)`

Text Solution

Verified by Experts

`underset(xto1)lim(x^(2)+xlog_(e)x-log_(e)x-1)/((x^(2))-1)" "(0/0"from")`
`=underset(xto1)lim((x-1)(log_(e)x+x+1))/((x+1)(x-1))" "(0/0"from")`
`=underset(xto1)lim(log_(e)x+x+1)/(x+1)`
`=(log_(e)1+1+1)/(1+1)=(0+2)/(2)=1`
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