Question

Is it true that $L_{f+g}(M)\le L_f(M)+L_g(M)$ if $M$ is a partition on [a,b] and $f, g$ are two bounded functions?

score 133 · Answer 1 · 2016-01-24 03:38:27

133

Views

Is it true that $L_{f+g}(M)\le L_f(M)+L_g(M)$ if $M$ is a partition on [a,b] and $f, g$ are two bounded functions?

Published on 24 Jan 2016 - 3:38

score 340 · Answer 2 · 2016-01-24 23:14:02

340

Views

Riemann-sum -> limit vs factorial/n-th root

Published on 24 Jan 2016 - 23:14

score 83 · Answer 3 · 2016-01-26 02:25:41

83

Views

Limit of trigonometric series and integrals

Published on 26 Jan 2016 - 2:25

score 71 · Answer 4 · 2016-01-26 17:15:15

71

Views

Any example for lower integral $\underline{I}_a^b (s)+\underline{I}_a^b (t)\ne \underline{I}_a^b (s+t) $ for two bounded functions $s$ and $t$?

Published on 26 Jan 2016 - 17:15

score 4k · Answer 5 · 2016-01-26 17:56:03

4k

Views

Riemann Integrability of Step Function

Published on 26 Jan 2016 - 17:56

score 446 · Answer 6 · 2016-01-26 20:10:23

446

Views

Express integral as limit of Riemann Sum. Then evaluate.

Published on 26 Jan 2016 - 20:10

score 69 · Answer 7 · 2016-01-29 04:46:06

69

Views

Real Analysis : Value of $U(f,P)-L(f,P)$ in Darboux Integral?

Published on 29 Jan 2016 - 4:46

score 651 · Answer 8 · 2026-03-29 21:52:13

651

Views

Assigning values to a divergent integral?

Published on 29 Mar 2026 - 21:52

score 119 · Answer 9 · 2016-01-31 22:07:20

119

Views

Riemann Sum-esque limit involving Radicals

Published on 31 Jan 2016 - 22:07

score 1.1k · Answer 10 · 2016-02-02 00:38:24

1.1k

Views

How to prove that if $f$ is integrable, then $\forall \epsilon >0, \ \exists$ partition $M\in [a,b]$ such that $U_f(M) - L_f(M)\lt\epsilon$?

Published on 02 Feb 2016 - 0:38

score 515 · Answer 11 · 2016-02-04 04:31:52

515

Views

Convert Riemann sum to definite integral: $\sum_{i = 1}^n \frac{n}{n^2 + i^2}$

Published on 04 Feb 2016 - 4:31

score 316 · Answer 12 · 2016-02-09 17:12:29

316

Views

Evaluation of $\lim_{n\rightarrow \infty}\sum_{k=1}^n\sin \left(\frac{n}{n^2+k^2}\right)$

Published on 09 Feb 2016 - 17:12

score 109 · Answer 13 · 2016-02-14 11:07:46

109

Views

$g(x) \ge 0$ Riemann integrable on $[a,b]$ then for each subinterval $\int^b_a g(x)dx \ge \int^d_c g(x)dx$

Published on 14 Feb 2016 - 11:07

score 1.1k · Answer 14 · 2016-02-24 09:30:00

1.1k

Views

Evaluating limit by relating it to Riemann sum

Published on 24 Feb 2016 - 9:30

score 1.6k · Answer 15 · 2016-02-24 17:42:22

1.6k

Views

Solve $\lim_{n\to \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{n+n}\right)$ without using Riemann sums.

Published on 24 Feb 2016 - 17:42

List Question

Is it true that $L_{f+g}(M)\le L_f(M)+L_g(M)$ if $M$ is a partition on [a,b] and $f, g$ are two bounded functions?

Riemann-sum -> limit vs factorial/n-th root

Limit of trigonometric series and integrals

Any example for lower integral $\underline{I}_a^b (s)+\underline{I}_a^b (t)\ne \underline{I}_a^b (s+t) $ for two bounded functions $s$ and $t$?

Riemann Integrability of Step Function

Express integral as limit of Riemann Sum. Then evaluate.

Real Analysis : Value of $U(f,P)-L(f,P)$ in Darboux Integral?

Assigning values to a divergent integral?

Riemann Sum-esque limit involving Radicals

How to prove that if $f$ is integrable, then $\forall \epsilon >0, \ \exists$ partition $M\in [a,b]$ such that $U_f(M) - L_f(M)\lt\epsilon$?

Convert Riemann sum to definite integral: $\sum_{i = 1}^n \frac{n}{n^2 + i^2}$

Evaluation of $\lim_{n\rightarrow \infty}\sum_{k=1}^n\sin \left(\frac{n}{n^2+k^2}\right)$

$g(x) \ge 0$ Riemann integrable on $[a,b]$ then for each subinterval $\int^b_a g(x)dx \ge \int^d_c g(x)dx$

Evaluating limit by relating it to Riemann sum

Solve $\lim_{n\to \infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{n+n}\right)$ without using Riemann sums.

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