consider two functions `f(x)=lim_(x->oo) (cos (x/sqrtn))^n` and `g(x)=-x^(4b)`, where `b=lim_(x->oo)(sqrt(x^2+x+1)-sqrt(x^2-1))`

Consider two function f(x)=lim_(n rarr oo)((cos x)/(sqrt(n)))^(n) and g(x)=-x^(4b) where b=lim_(x rarr oo)(sqrt(x^(2)+x+1)-sqrt(x^(2)+1))* then f(x) is and number of solutions of f(x)+g(x)=0 is

lim_(x->oo)x^(3/2)(sqrt(x^3+1)-sqrt(x^3-1))

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

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

lim_(x->oo) (x-sqrt(x^2-1))

lim_(x rarr oo)(sqrt(x+1)-sqrt(x))

lim_(x rarr oo)(sqrt(x+1)-sqrt(x))

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

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

lim_(x rarr oo)sqrt(x+1)-sqrt(x)