1. Gradient practice.Compute the gradients of the following functions finCartesian, cylindrical, and spherical coordinates. For the non-Cartesian coordinate systems,first use the formula for the gradient in terms of the non-Cartesian unit vectors, and then usethe conversions between the unit vectors to convert your answer back to Cartesian coordinates.In all cases, you should find the same answer independent of the coordinate system! (You willfind that, for all of these examples, the gradient is easy in one coordinate system but a messin at least one of the others; this illustrates the value of choosing a good set of coordinatesfor the problem at hand.)(a) f(x, y, z) = x² + y² + ₂²(b) f(x, y, z) = sin z(c) f(x, y, z)=x+y+z2. Divergence practice.Compute the divergences of the following vector fieldsv in the given coordinate systems, 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 finalanswer back to Cartesian coordinates.(a) v = xx+yŷ + zz: Cartesian, cylindrical, spherical(b) vp: Cartesian, cylindrical(c) v = 0: Cartesian, spherical

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