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((e^(x) sin y)/y) , if the limit exists.

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

lim _((x,y) to(1,0))(x ^(2) + y ^(2))/(x - 2y ) is :

Let g(x,y) = (x^(2)y)/(x^(4) + y^(2)) for (x,y) ne (0,0) and f(0,0)=0. (i) Show that lim_((x,y) to (0,0)) g(x,y)=0 along every line y=mx, m in R . (ii) Show that lim_((x,y) to (0,0)) g(x,y) = k/(1+k^(2)) , along every parabola y=kx^(2), k in R{0} .