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

Evaluate lim_((x,y) to (0,0)) cos((e^(x) sin y)/y) , if the limit exists.

Evaluate: lim_((x,y)->(0,0))(x^(3)y)/(x^(4)+y^(4))

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 the limits lim_(x to 0) (1+x)^(1//3x)

Evaluate the limits lim_(x to 0) (2^x-3^x)/x

Evaluate the limits lim_(x to 0) (2arcsinx)/(3x)

Evaluate the following limits : Lim_(x to 0) (3^(x)-1)/x