Please convert to spherical coordinates (withsimplification) to solve.
- Please Convert To Spherical Coordinates With Simplification To Solve 1 (41.73 KiB) Viewed 10 times
(1) Consider the function f: R³ → R given by f(x, y, z) = where k is a positive constant. sin(x + y) cos(z) √x² + y² + z² 0 lim (x,y,z) 0 4 if (x, y, z) (0, 0, 0), if (x, y, z) = (0, 0, 0), (a) Find all values of k> 0 for which f is continuous at the origin. In other words, find all positive real numbers k for which sin(x + y) cos(z) √x² + y² + z² = 0.
(b) Find all values of k> 0 for which fz (0, 0, 0) exists. In other words, find all positive real numbers k for which lim t-0 f(t,0,0)-f(0, 0, 0) t exists and is finite. For each such value, what is fa (0, 0, 0)? (c) What are f(0, 0, 0) and f, (0, 0, 0)? Do those values depend on k?