Evaluate `lim_((x,y) to (1,2))`, g(x,y) , if the limit exist where g(x,y) `=(3x^(2) - xy)/(x^(2) + y^(2)+ 3)`

Evaluate lim_((x,y) to (0,0)) cos((x^(3) + y^(3))/(x+y+2)) . If the limit exists.

Evaluate : 3x^(2) + 5xy - 4y^(2) + x^(2) - 8xy - 5y^(2)

If x=2+3i and y=2-3i then find the values of : (x^(2)+xy+y^(2))/(x^(2)-xy+y^(2))

What is ((x^(2)+y^(2))(x-y)-(x-y)^(3))/(x^(2)y-xy^(2)) equal to ?

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?