`lim_(x->0)(xsqrt(y^2-(y-x)^2))/{sqrt(8xy-4x^2)+sqrt(8xy)}^3 =`

lim_(x rarr0)(x sqrt(y^(2)-(y-x)^(2)))/({sqrt(8xy-4x^(2))+sqrt(8xy)}^(3))=

lim_(xrarr0)(xy(sqrt(y^(2)-(y-x)^(2))))/((sqrt(8xy-4x^(2))+sqrt(8xy))^(3))" equals"

lim_(x rarr 0) (sqrt(8-3x)+sqrt(8+4x))/(sqrt(2-3x))= _______.

Evaluate lim_(xtooo) x^(3){sqrt(x^(2)+sqrt(1+x^(4)))-xsqrt(2)}.

lim_(x rarr sqrt(2)) ((x^2 - 4)/(x^2 + 3sqrt(2)x - 8))

If x,y in R satisfy the equation x^(2)+y^(2)-4x-2y+5=0, then the value of the expression ((sqrt(x)-sqrt(y))^(2)+4sqrt(xy))/((x+sqrt(xy))) is

The value of f(x,y)=((4sqrt(x^(3)y)-4sqrt(x^(3)))/(sqrt(y)-sqrt(x))+(1+sqrt(xy))/(4sqrt(xy)))^(-2)(1+2sqrt((y)/(x))+(y)/(x))^((1)/(2)) when x=9,y=0.04

(sqrt(x)+sqrt(y))^(2)=x+y+2sqrt(xy) and sqrt(x)sqrt(y)=sqrt(xy) , where x and y are positive real numbers . If x=2sqrt(5)+sqrt(3) and y=2sqrt(5)-sqrt(3) , then x^(4)+y^(4) =