Evaluate the limit: `("lim")_(xvecoo)[sqrt(a^2x^2+a x+1)-sqrt(a^2x^2+1)]`

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

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

Evaluate the following limits : lim_(x to 0)(sqrt(a^(2)+x^(2))-sqrt(a^(2)-x^(2)))/x^(2).

Evaluate the following limit: (lim)_(x rarr oo)(sqrt(x^(2)+a^(2))-sqrt(x^(2)+b^(2)))/(sqrt(x^(2)+c^(2))-sqrt(x^(2)+d^(2)))

Evaluate the following limit: (lim)_(x->9)(3-sqrt(x))/(4-sqrt(2x-2))

Evaluate the following limits : lim_(x to 0)(sqrt(x+2)-sqrt(2))/x

Evaluate the following limit: (lim)_(x rarr0)(sqrt(1+x^(2))-sqrt(1-x^(2)))/(x)

Evaluate the following limits : lim_(x to infty)(sqrt(x^(2)+x+1)-sqrt(x^(2)+1)) .

Evaluate the following limit: (lim)_(x rarr2)(sqrt(x^(2)+1)-sqrt(5))/(x-2)

Evaluate the following limit: (lim)_(x rarr0)(1sqrt(+x+x^(2))-sqrt(x+1))/(2x^(2))