Define f : R" - ||x ||<) +7² _if ||x || < 1 and f(x) [0, 0) by letting f(x) = if ||x|| > 1. Prove that f is continuous on R". (To prove that f is continuous at a given xo E R™, consider separately the following three cases: ||x0|| > 1, ||x0|| < 1, ||o|| = 1.) = 0

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