洞察力
发表于 2025-3-23 12:56:05
Functions of Bounded Variation,ce between either sum and the integral is at most ., the oscillatory sum corresponding to ...Thus the oscillatory sum is an upper bound for the difference between the approximating sums and the integral..We also know that if . is integrable, then the oscillating sum can become smaller than any fixed
反馈
发表于 2025-3-23 14:04:32
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affect
发表于 2025-3-23 19:24:20
The Improper Integral,nts of the interval) and are bounded on that interval. These restrictions are sometimes too strict; there are problems whose solutions require us to integrate functions on unbounded intervals, or that themselves might not be bounded.
cuticle
发表于 2025-3-24 01:25:46
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Bronchial-Tubes
发表于 2025-3-24 03:46:46
The Definite Integral,This concept, in contrast to that of the indefinite integral, assigns numbers to functions (and not a family of functions). In the next chapter, we will see that as the name . that they share indicates, there is a strong connection between the two concepts of integrals.
bisphosphonate
发表于 2025-3-24 09:43:34
Functions of Bounded Variation,ence between the approximating sums and the integral..We also know that if . is integrable, then the oscillating sum can become smaller than any fixed positive number for a sufficiently fine partition (see Theorem 14.23).
大包裹
发表于 2025-3-24 12:30:10
Infinite Sequences II, that is, .. ≠ 0 for all . > .., then 1 ≤ .. ≤ 9, and so . also holds if . > ... By Theorem 4.17, .. Thus for a given . > 0, there is an .. such that . for all . > ... So if ., then ., and thus .. → 1.
burnish
发表于 2025-3-24 15:49:08
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社团
发表于 2025-3-24 21:55:54
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Blasphemy
发表于 2025-3-24 23:12:25
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