Abstract
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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© 1991 Springer Science+Business Media New York
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Protter, M.H., Morrey, C.B. (1991). Continuity and Limits. In: A First Course in Real Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8744-0_2
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DOI: https://doi.org/10.1007/978-1-4419-8744-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6460-6
Online ISBN: 978-1-4419-8744-0
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