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

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

Discussion

`lim_(xto oo) (1)/(n) {1+e^(1//n)+e^(2//n)+e^(3//n)+.....+e^((n-1)/(n))}` is equal toA. eB. `-e`C. `e-1`D. `1-e`
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`lim_(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x)` , isA. 2B. `-(1)/(2)`C. `(1)/(2)`D. `-2`
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`lim_(xrarroo) ((x+2)/(x+1))^(x+3)` is equal toA. 1B. eC. `e^2`D. `e^3`
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