Evaluate `lim_(ntooo) (1)/(n^(2(log_(e)n-log_(e)(n-1)))+n)`.

1.	Evaluate `lim_(ntooo) (1)/(n^(2(log_(e)n-log_(e)(n-1)))+n)`.
Answer» `underset(ntooo)lim(1)/(n^(2(log_(e)n-log_(e)(n-1)))+n)` `=underset(ntooo)lim(1)/(n^(2)("log"_(e)(n)/(n+1))+n)` `=underset(ntooo)lim(1)/(n^(2)("log"_(e)(1)/(1+(1)/(n)))+n)` `=underset(xto0)lim(1)/((1)/(x^(2))("log"_(e)(1)/(1+x))+(1)/(x))` `=underset(xto0)lim(1)/(-(log_(e)(1+x))/(x^(2))+(1)/(x))` `=underset(xto0)lim(x^(2))/(x-log_(e)(1+x))` `=underset(xto0)lim(x^(2))/(x-(x-(x^(2))/(2)))=2`

Discussion

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If `lim_(xto oo){(x^2+1)/(x+1)-(ax+b)}to oo`, thenA. `a in (1,oo)`B. `a ne 1 , b in R`C. `a in (-oo,1)`D. none of these
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`lim_(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x)` , isA. 2B. `-(1)/(2)`C. `(1)/(2)`D. `-2`
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