The density throughout a composite material is given by $T(x, y, z) = Axy^2 + Bxz^3 + Cy^2z^3,$ where $x$, $y$ and $z$ are the cartesian coordinates of the position inside the material.
(a) Find the dimensions of $A$, $B$ and $C$.
given this equation i guess that the conditions at the limits are given ( something like T(0,y,z)= ? or T(x,0,z) = ? or T(x,y,0)= ? ) well if you have one of these you just have to make a derivation by x or y or z. or replacing the values of x or y or z. and test all the cases and normally it should be resolved.