" 0."(x+2)/(sqrt(4x-x^(2)))

Let f(x) be defined in [-2,2] by f(x)={max(sqrt(4)-x^(2)),sqrt(1+x^(2))),-2<=x<=0;min(sqrt(4-x^(2)),sqrt(1+x^(2)),0

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

lim_(x rarr0)(x sqrt(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))=

int_(0)^(2)x^(2)sqrt(4-x^(2))dx=

Show that Lt_(x to-2) sqrt(x^(2)-4)=0= Lt_(x to 2) sqrt(x^(2)-4)

Let f(x)+f(y)=f(x sqrt(1-y^(2))+y sqrt(1-x^(2)))[f(x) is not identically zerol.Then f(4x^(3)-3x)+3f(x)=0f(4x^(3)-3x)=3f(x)f(2x sqrt(1-x^(2))+2f(x)=0f(2x sqrt(1-x^(2))=2f(x)

lim_(x rarr0)(x)/(sqrt(x+4)-2)