Question

Why does choosing $\varepsilon$ to be arbitrarily small mean equality?

score 907 · Answer 1 · 2016-11-04 05:19:02

907

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Why does choosing $\varepsilon$ to be arbitrarily small mean equality?

Published on 04 Nov 2016 - 5:19

score 77 · Answer 2 · 2016-11-04 18:51:38

77

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If $f(x)= \lim_ {n \to \infty} \sum_{r=1}^{n} \frac{n}{n^2+x^2r^2}$, find the required value

Published on 04 Nov 2016 - 18:51

score 127 · Answer 3 · 2026-02-23 04:58:21

127

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$f(x) = x^2$. For each positive integer $n$, let $P_n$ be the partition $P_n = \{0, \frac{1}{n}, \frac{2}{n},..., \frac{n-1}{n},1 \}$ of $[0,1]$.

Published on 23 Feb 2026 - 4:58

score 2.1k · Answer 4 · 2026-02-23 04:58:22

2.1k

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Show $f$ is integrable in each subinterval, $[x_{i−1}, x_i]$, and further, $\int_a^bfdx=\sum^n_{k=1}\int\limits_{x_{k-1}}^{x_k}fdx$.

Published on 23 Feb 2026 - 4:58

score 312 · Answer 5 · 2016-11-06 17:14:45

312

Views

Fourier Series Problem and Convergence

Published on 06 Nov 2016 - 17:14

score 4.5k · Answer 6 · 2016-11-08 00:48:30

4.5k

Views

Evaluate the Riemann sum

Published on 08 Nov 2016 - 0:48

score 65 · Answer 7 · 2016-11-08 20:05:19

65

Views

Riemann Sum Question Help Needed

Published on 08 Nov 2016 - 20:05

score 95 · Answer 8 · 2016-11-09 02:46:02

95

Views

Expressing Limit as Riemann Integral

Published on 09 Nov 2016 - 2:46

score 62 · Answer 9 · 2016-11-09 09:08:20

62

Views

Problem with finding the limit using integral and summation

Published on 09 Nov 2016 - 9:08

score 85 · Answer 10 · 2016-11-12 10:50:49

85

Views

Proving that the existence of given limit implies that bounded $f:[a,b]\to\mathbf R$ is Riemann integrable

Published on 12 Nov 2016 - 10:50

score 49 · Answer 11 · 2016-11-15 00:46:59

$\lim_{N \to \infty} \frac{4}{\pi} \sum_{ k > 0, \ k \text{ odd }}^{N} \frac{\sin({\frac{k\pi}{N+1}})}{k} = $ Gibbs konstant

score 282 · Answer 12 · 2016-11-18 13:32:56

282

Views

Is integrability metric-dependent?

Published on 18 Nov 2016 - 13:32

score 116 · Answer 13 · 2016-11-18 21:53:16

116

Views

Working with square roots

Published on 18 Nov 2016 - 21:53

score 506 · Answer 14 · 2016-11-19 00:26:11

506

Views

Distance Between 2 Points on a Given function

Published on 19 Nov 2016 - 0:26

score 495 · Answer 15 · 2016-11-20 13:43:58

495

Views

Alternate definition for upper/lower integrals

Published on 20 Nov 2016 - 13:43

List Question

Why does choosing $\varepsilon$ to be arbitrarily small mean equality?

If $f(x)= \lim_ {n \to \infty} \sum_{r=1}^{n} \frac{n}{n^2+x^2r^2}$, find the required value

$f(x) = x^2$. For each positive integer $n$, let $P_n$ be the partition $P_n = \{0, \frac{1}{n}, \frac{2}{n},..., \frac{n-1}{n},1 \}$ of $[0,1]$.

Show $f$ is integrable in each subinterval, $[x_{i−1}, x_i]$, and further, $\int_a^bfdx=\sum^n_{k=1}\int\limits_{x_{k-1}}^{x_k}fdx$.

Fourier Series Problem and Convergence

Evaluate the Riemann sum

Riemann Sum Question Help Needed

Expressing Limit as Riemann Integral

Problem with finding the limit using integral and summation

Proving that the existence of given limit implies that bounded $f:[a,b]\to\mathbf R$ is Riemann integrable

$\lim_{N \to \infty} \frac{4}{\pi} \sum_{ k > 0, \ k \text{ odd }}^{N} \frac{\sin({\frac{k\pi}{N+1}})}{k} = $ Gibbs konstant

Is integrability metric-dependent?

Working with square roots

Distance Between 2 Points on a Given function

Alternate definition for upper/lower integrals

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