Prove that f is continuous at xo if and only if limo—co Pry') = f (x0) for every sequence (x„) —* xo. How would you expect this characterization of continuity at xo to be modified if xo is not an interior point of its domain? 5.4.1 Refer to Example 5.28. Let
G(x) 1—F(x) if x 0 if x = O.
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Continuous Functions Chapter
Show that G has the IVP, yet F + G does not. Thus the class of functions with IVP is not closed under addition.
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