`lim_(x->oo) (sqrt(x^2+x)-x)`

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

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

The value of the limit lim_(x to -oo) (sqrt(4x^(2) - x )+2x) is

Evaluate the following limit: (lim)_(x->+-oo)(sqrt(x^2-2x-1)-sqrt(x^2-7x-3))

Evaluate the following limit: (lim)_(x rarr-oo)(sqrt(x^(2)-8x)+x)

Let L_(1)=lim_(x rarr0)((sin(2x)+cos(x)-1)/(x)) , L_(2)=lim_(x rarr oo)(sqrt(x^(2)-x)-x) , and L_(3)=lim_(x rarr4)(x^(2)-3x)/(x^(2)-x) , then the value of L_(1)L_(2)+(1)/(L_(3)) is

If (lim)_(x->oo)(sqrt((x^4-x^2+1))-a x^2-b)=0 , then there exists at least one a\ a n d\ b for which point (a,-2b) lies on the line.

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

Show that lim_(x rarr oo){sqrt(x^(2)+x)-x}=(1)/(2)

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