If `lim_(x->oo)x^a(sqrt(x^2+sqrt(x^4+1))-sqrt(2x))` exists and has value non-zero finite real aumber L, then find the value of `alpha/L^2`.

If lim_(x rarr oo)x^(alpha)(sqrt(x^(2)+sqrt(x^(4)+1))-sqrt(2)x) exists and has value non-zero finite real number L, then the largest prime factor of (alpha)/(L^(2)) is

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

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

lim_(xto oo)(sqrt(4x^(2)+2x+1)-sqrt(4x^(2)+1)) is

lim_(xrarr oo)(sqrt(3x^2-1)+sqrt(2x^2-1))/(4x+3)=

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

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

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

If the lim_(x rarr0)(1)/(x^(3))((1)/(sqrt(1+x))-(1+ax)/(1+bx)) exists and has the value equal to l, then find the value of (1)/(a)-(2)/(l)+(3)/(b)

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