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

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))

Evaluate: lim_(x rarr oo)(sqrt(3x^(2)-1)-sqrt(2x^(2)-1))/(4x+3)

The value of lim_(x rarr oo)(sqrt(x^(2)+x+1)-sqrt(x^(2)-x+1) equal to

The value of lim_(x rarr oo)(sqrt(x^(2)+x+1)-sqrt(x^(2)-x+1)) equals

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

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

lim_(x rarr oo)((sqrt(x^(2)+5)-sqrt(x^(2)-3))/(sqrt(x^(2)+3)-sqrt(x^(2)+1)))

lim_(x rarr oo)((sqrt(1+25x^(2))+sqrt(9x^(2)-1))/(sqrt(1+25x^(2))-sqrt(9x^(2)-1)))=