Unformatted text preview: ii) Show that f is discontinuous at x n = 0. iii) Show that f is di²erentiable at x = 0. 3. Prove (iii) of Corollary 29.7. 4. Let f : R → R and di²erentiable on R . Suppose sup x ∈ R { f ′ ( x ) } = M < 1. Take s ∈ R and de±ne a sequence s n +1 = f ( s n ) n = 0 , 1 , 2 , . . .. Then, show that { s n } is a Cauchy sequence. Hint: Show ±rst that  s n +1 − s n  ≤ M  s n − s n − 1  . 1...
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 Fall '07
 Fukuda
 Derivative, Mathematical analysis, Continuous function, MAT 125A Homework, R. Suppose supxR

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