Continuity and limits
Most of the functions we study in elementary calculus are described by simple formulas. These functions almost always possess derivatives and, in fact, a portion of any first course in calculus is devoted to the development of routine methods for computing derivatives. However, not all functions possess derivatives everywhere. For example, the functions (1 + x2)/x, cot x, and sin(1/x) do not possess derivatives at x = 0 no matter how they are defined at x = 0.
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