l. Gradient practice. [all] points} Compute the gradients of the following functions f in lCartesian1 cylindrical, and spherical coordinates. For the non-Cartesian coordinate systems? rst use the formula for the gradient in terms of the non-Cartesian unit vectors. and then use the conversions between the unit vectors to convert your answer hack to Cartesian coordinates. In all cases. you should find the same answer independent of the coordinate system! {You will nd that1 [or all of these examples? the gradient is easy in one coordinate system but a mess in at least one of the others; this illustrates the value of choosing a good set of coordinates for the problem at hand.) (a) re. a z} = v\" + v? + 2-2 (bl Heinz} = sin: {Cl III1y12l=I+v+z 2. Divergence practice. {4D points} lCompute the divergences oI the following vector elds v in the given coordinate systems1 checking as in problem 1 that you get the same answer [which should just be a scalar function} in all coordinate systems by converting your final answer hack to Cartesian coordinates. [a] v = t + y? + 2%: Cartesian. cylindrical, spherical {h} v = Er: Cartesian, cylindrical E}: {c} v = Cartesian. spherical