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

Show that lim_(x rarr oo)(sqrt(x^(2)+x+1)-x)!=lim_(x rarr oo)(sqrt(x^(2)+1)-x)

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

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

[" Which of the following limit is "],[" not finite: "],[" (1) "lim_(x rarr0^(+))(cot x)^((sin x-x)/(x^(4)))],[" (2) "lim_(x rarr0^(+))(cot x)^((x^(3))/(sin x-x))],[" (3) "lim_(x rarr oo)(sqrt(x^(2)+1)-x)],[" (4) "lim_(x rarr0)(sin x)/(x^(2))]

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

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

Evaluate: lim_(x rarr oo)(sqrt(x^(2)+1)-x^(3)+13)/(x^(4)+14-x^(4)+15)

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

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

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