## Differential and integral calculus |

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absolutely convergent arc tg assertion bounded CHAPTER CHELSEA SCIENTIFIC BOOKS continuous at f continuous everywhere continuous function convergent series converges absolutely converges everywhere converges uniformly cos2 defined definite integral Definition 90 differentiable diverges dx exist entire rational function equation example to Theorem exists a p exists exactly f(x)dx exist ff(x)dx finite number fn(x given holds hypotheses of Theorem hypothesis improper integral independent infinite series infinitely integral calculus interval jbf(x left-hand side Let f(x lim f(x limit point monotonically notation Obvious by Theorem Originally published otherwise polynomial positive integers Preliminary Remark proof of Theorem properly integrable prove real numbers Riemann condition right-hand side sense of Theorem sequence series converges set of numbers side is meaningful sub-interval suitable Theorem 159 Theorem 27 Theorem 335 theory ultimately uniformly convergent v=l v=l wording