Thus to evaluate a triple integral in cylindrical coordinates, we do the following: (i) Convert the function f(x,y,z) into a cylindrical function. (ii) Convert the projection D into a polar region. (iii) Change the limits of the integral and include the “r” in the integral. (iv) Evaluate. We illustrate with some examples. Example 2.1. Aug 08, 2016 · Spherical form+ r=cos phi csc^2 theta. Cylindrical form: r=z csc^2theta The conversion formulas, Cartesian to spherical:: (x, y, z)=r(sin phi cos theta, sin phi sin theta, cos phi), r=sqrt(x^2+y^2+z^2) Cartesian to cylindrical: (x, y, z)=(rho cos theta, rho sin theta, z), rho=sqrt(x^2+y^2) Substitutions in x^2+y^2=z lead to the forms in the answer. Note the nuances at the origin: r = 0 is ...

We can calculate the dot product for any number of vectors, however all vectors must contain an equal number of terms. Example Find a ⋅ b when a = <3, 5, 8> and b = <2, 7, 1>

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