If `f(x)={{:(sinx","" "xnenpi", "ninI),(2","" ""otherwise"):}` and `g(x)={{:(x^(2)+1","" "xne0", "2),(4","" "x=0),(5","" "x=2):}` then find `lim_(xto0) g{f(x)}`.

If `f(x)={{:(sinx","" "xnenpi", "ninI),(2","" ""otherwise"):}` and `g(

1.	If `f(x)={{:(sinx","" "xnenpi", "ninI),(2","" ""otherwise"):}` and `g(x)={{:(x^(2)+1","" "xne0", "2),(4","" "x=0),(5","" "x=2):}` then find `lim_(xto0) g{f(x)}`.
Answer» Correct Answer - 1 `underset(xto0^(+))limg{f(x)}=g(f(0^(+)))=g((sin0^(+)))=g(0^(+))=(0)^(2)+1=1` `underset(xto0^(-))limg{f(x)}=g(f(0^(-)))=g((sin0^(-)))=g(0^(-))=(0)^(2)+1=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
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\(f\left(x\right)=\left[\left(\frac{min\left(t^2+4t+6\right)\sin \left(x\right)}{x}\right)\right]\)where [.] represents greatest integer function, then find \(\lim _{x\to 0}\left(f\left(x\right)\right)\)
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