20. Let f be a function of three variables that is continuous everywhere. (a) Explain why the function f(x,y,z) is continuous if and x+y+z only if x + y + z # 0. (b) Use Definition 12.15 to explain why f(x,y,z) lim (x,y,z)→ (a,b,–(a+b)) x+y+z does not exist for any pair (a, b) of real numbers.

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