Evaluate `lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.`

1.	Evaluate `lim_(ntooo) (n^(p)sin^(2)(n!))/(n+1),"wher "0ltplt1.`
Answer» We have `underset(ntooo)lim(n^(p)sin^(2)(n!))/(n+1)" "((oo)/(oo)"from")` `=underset(ntooo)lim(sin^(2)(n!))/(n^(1-p)(1+1/n))` `=("some number between 0 and1")/(ooxx1)=0" "("as "0ltplt1)`

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
Evaluate:\(\lim\limits_{x \to 1}\frac{\sqrt {1+x}-\sqrt {1-x}}{1+x}\)
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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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`lim_(x->0)((1-cos2x)sin5x)/(x^2sin3x)`A. `10//3`B. `3//10`C. `6//5`D. `5//6`