(a) Prove that f+(x) ~ 0, f-(x) ~ 0, f(x) = f+(x) - f-(x), and If(x)1 =...
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(a) Prove that f+(x) ~ 0, f-(x) ~ 0, f(x) = f+(x) - f-(x), and If(x)1 =
f+(x) + f-(x) hold for all x E Dom (f). (Compare with Exercise 1, p. 11.)
(b) Prove that if L = lim f(x)
x-->a exists, then f+ (x) ---; L + and
f- (x) ---; L - as x ---; a.
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