`lim_(n rarr oo){(sqrt(5)+2)^(n)}*cos(pi[(sqrt(5)+2)^(n)]` is equal to (where `n in I` and `[], {.}` denotes greatest integer function and fractional part function respectively)

Let f (x)= tan/x, then the value of lim_(x->oo) ([f(x)]+x^2)^(1/({f(x)})) is equal to (where [.] , {.} denotes greatest integer function and fractional part functions respectively) -

If f(x)=[x^(2)]+sqrt({x}^(2)), where [] and {.} denote the greatest integer and fractional part functions respectively,then

lim_(n rarr oo) sqrt(n)/sqrt(n+1)=

lim_(n rarr oo)(sqrt(n+1)-sqrt(n))=0

Evaluate the following limits ([.],{.} denotes greatest integer function and fractional part respectively) lim_(x rarr0)cot^(-1)x^(2)

lim_(n rarr oo)(1+sqrt(n))/(1-sqrt(n))

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is

lim_(n rarr oo)(sqrt(n^(2)+n)-sqrt(n^2+1))

The function f(x)=[x]+sqrt({x}), where [.] denotes the greatest Integer function and {.} denotes the fractional part function respectively,is discontinuous at

Evaluate the following limits ([.],~ {.}~ denotes~ greatest integer function and fractional part respectively) (lim)_(x rarr n)[x],(lim)_(x rarr n){x},n in I