lim_(n rarr oo)(cos(x)/(sqrt(n)))^(n)" is "

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

consider two functions f(x)=lim_(x 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))

lim_(n rarr oo)(3+sqrt(n))/(sqrt(n))

lim_(n rarr oo)(1+(x)/(n))^(n)

lim_(n rarr oo)(sin(1)/(sqrt((n))))((1)/(sqrt(n+1)))^(+(1)/(sqrt(n+2))+(1)/(sqrt(n+2)))

lim_(n rarr oo)2^(1/n)

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

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

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

lim_(n rarr oo)(2^(3n))/(3^(2n))=