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

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

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

lim_(x rarr oo)(sqrt(x-a)-sqrt(x-b))

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))

lim_(x rarr oo)(sqrt(x)-3)/(sqrt(x)+3)

lim_(x rarr oo)(sqrt(x)-sqrt(x-3))

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

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

Prove that: lim_(x rarr oo)x(sqrt(x^(2)+1)-sqrt(x^2-1))) = 1