(e) On the axes provided in Figure 1.7.3, sketch an accurate, labeled graph of \(y = f (x)\). None of the above properties hold in general for functions that are discontinuous.F ( x ) \neq f ( a )\] pair of distinct approaches to justifying the calculus: Leibniz considered two dierent approaches to the foun-dations of the calculus one connected with the classical methods of proof by exhaustion, the other in connec-tion with a law of continuity (Bos 5, item 4.2, p. Then if g ( p ) ≠ 0, f g x is continuous at x = p.Ĭomposition of continuous functions: If g ( x ) is continuous at x = p, and f ( x ) is continuous at g ( p ), then f g ( x ) = f ∘ g ( x ) is continuous at x = p.
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