If g(x,y)=x2yx4+y2{“version”:”1.1″,”math”:”g(x,y)=x2yx4+y2″}…

If g(x,y)=x2yx4+y2{“version”:”1.1″,”math”:”g(x,y)=x2yx4+y2″}, determine lim(x,y)→(0,0)g(x,y){“version”:”1.1″,”math”:”lim(x,y)→(0,0)g(x,y)”} by looking at various paths.  Enter DNE if the limit does not exist. (a) Along the path  (b) Along the path (c) Along the path  From the various paths, we can conclude that The limit is …. The limit does not exist. _______

Consider the following functions: w=w(x,y,z)=3×2-2xy+4z2x=x(…

Consider the following functions: w=w(x,y,z)=3×2-2xy+4z2x=x(s,t)=es sin(3t)y=y(s,t)=es cos(2t)z=z(s,t)=e2s{“version”:”1.1″,”math”:”w=w(x,y,z)=3×2-2xy+4z2x=x(s,t)=es sin(3t)y=y(s,t)=es cos(2t)z=z(s,t)=e2s”} Draw the tree diagram and find ∂x∂s, ∂x∂t, ∂y∂s, ∂y∂t, ∂z∂s, ∂z∂t{“version”:”1.1″,”math”:”∂x∂s, ∂x∂t, ∂y∂s, ∂y∂t, ∂z∂s, ∂z∂t”}.  Then find ∂w∂s, ∂w∂t{“version”:”1.1″,”math”:”∂w∂s, ∂w∂t”} using a chain rule.  Simplify your answer.  _______