Chapter 3

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In particular, f is discontinuous at c ∈ A if there is sequence (xn) in the domain A of f such that xn → c but f(xn) ̸→f(c). Let’s consider some examples of continuous and discontinuous functions to illustrate the definition. Example 3.7. The function f: [0,∞) → R defined by f(x) = √ x is continuous on [0,∞).

  Continuous, Discontinuous