`lim_(xto1) [cosec(pix)/(2)]^(1//(1-x))` (where `[.]` represents the greatest integer function) is equal toA. (i) exists, (ii) does not existB. (i) does not exist, (ii) existsC. both (i) and (ii) existD. neither (i) nor (ii) exists

`lim_(xto1) [cosec(pix)/(2)]^(1//(1-x))` (where `[.]` represents the g

1.	`lim_(xto1) [cosec(pix)/(2)]^(1//(1-x))` (where `[.]` represents the greatest integer function) is equal toA. (i) exists, (ii) does not existB. (i) does not exist, (ii) existsC. both (i) and (ii) existD. neither (i) nor (ii) exists
Answer» Correct Answer - B `cosec(pix)/(2)to1^(+)" when "xto1` or`[cosec(pix)/(2)]=1 `:." ""limit "=1`

`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`
`lim_(xto oo) ((nsqrt(a)+nsqrt(b))/(2))^n,a,b,gt 0` equalsA. 1B. `sqrt(pq)`C. `pq`D. `(pq)/(2)`
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:\(\lim\limits_{x \to 1}\frac{\sqrt {1+x}-\sqrt {1-x}}{1+x}\)
\(f\left(x\right)=\left[\left(\frac{min\left(t^2+4t+6\right)\sin \left(x\right)}{x}\right)\right]\)where [.] represents greatest integer function, then find \(\lim _{x\to 0}\left(f\left(x\right)\right)\)
`lim_(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x)` , isA. 2B. `-(1)/(2)`C. `(1)/(2)`D. `-2`
The value of `lim_(xrarroo) ((x+3)/(x-1))^(x+1)` isA. eB. `e^2`C. `e^4`D. `1//e`
`lim_(xrarroo) ((x+2)/(x+1))^(x+3)` is equal toA. 1B. eC. `e^2`D. `e^3`
`lim_(x->0)((1-cos2x)sin5x)/(x^2sin3x)`A. `(10)/(3)`B. `(3)/(10)`C. `(6)/(5)`D. `(5)/(6)`
`lim_(x->0)((1-cos2x)sin5x)/(x^2sin3x)`A. `10//3`B. `3//10`C. `6//5`D. `5//6`