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

lim_( x to 0)(xsqrt(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"

Prove that lim_(xto0)(xsqrt(2ax-x^(2)))/((sqrt(8ax-4x^(2))+sqrt(8ax))^(3))=(1)/(128a)

lim_(x rarr 0) (x sqrt(y^(2) - (y - x)^(2)))/((sqrt(8xy - 4x^(2)) + sqrt(8xy))^(3)) equals :

If x>y prove that sqrt(y+sqrt(2xy-x^2))+sqrt(y-sqrt(2xy-x^2)) = sqrt(2x) .

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

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

Evaluate the following limits : Lim_(x to sqrt(2))(x^(4)-4)/(x^(2)+3xsqrt(2)-8)