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Calculus, how to find the value of delta in $\epsilon$-$\delta$ limit proof

score 2.3k · Answer 1 · 2026-04-13 21:34:15

2.3k

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Calculus, how to find the value of delta in $\epsilon$-$\delta$ limit proof

Published on 13 Apr 2026 - 21:34

score 388 · Answer 2 · 2026-04-17 05:29:06

388

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Evaluating $\lim_{x\rightarrow 0}\frac{\cos(ax) - \cos(bx)}{\sin^2(x)}$

Published on 17 Apr 2026 - 5:29

score 37 · Answer 3 · 2026-04-15 23:41:56

37

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For $\{x_n\}\in X$ do we always have $\lim_{n\to\infty}\|x_n\| = 0 \quad \text{iff}\quad\lim_{n\to \infty}x_n=0?$

Published on 15 Apr 2026 - 23:41

score 500 · Answer 4 · 2026-04-14 19:22:06

500

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Prob. 2, Sec. 3.3, in INTRO. TO REAL ANALYSIS by Bartle & Sherbert: What is the limit of this sequence?

Published on 14 Apr 2026 - 19:22

score 142 · Answer 5 · 2026-04-16 12:34:35

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$\lim_{x\rightarrow\infty}p\left(x\right)^{\frac{1}{\ln x}}$ where $p(x)$ is a polynomial of degree $n$

Published on 16 Apr 2026 - 12:34

score 822 · Answer 6 · 2026-04-13 04:08:40

822

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Proof Verification: $\frac{(-1)^{n}n}{n+1}$ diverges

Published on 13 Apr 2026 - 4:08

score 76 · Answer 7 · 2026-04-12 22:47:13

76

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Limit of shifted indexes pairs series

Published on 12 Apr 2026 - 22:47

score 48 · Answer 8 · 2026-04-12 10:24:46

48

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Upper bound for limsup

Published on 12 Apr 2026 - 10:24

score 124 · Answer 9 · 2026-04-10 19:21:43

124

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Limits of sub sequences

Published on 10 Apr 2026 - 19:21

score 3.6k · Answer 10 · 2026-04-13 23:54:32

3.6k

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If $\,\lim_{h\to 0}\frac{f(x+h)-f(x-h)}{2h}\,$ exists for every $x$, what does this imply for $f$?

Published on 13 Apr 2026 - 23:54

score 385 · Answer 11 · 2026-04-11 01:34:42

385

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Limit simplification

Published on 11 Apr 2026 - 1:34

score 416 · Answer 12 · 2026-04-15 19:09:57

416

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Computing the Limits $ (1) \lim_{n \rightarrow \infty} \frac{10^n}{n!} ~~ (2) \lim_{n \rightarrow \infty} \frac{n^n}{n!} $

Published on 15 Apr 2026 - 19:09

score 46 · Answer 13 · 2026-04-09 16:35:03

46

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How to approximate a function involving arc-tangent for a sufficiently large argument?

Published on 09 Apr 2026 - 16:35

score 528 · Answer 14 · 2026-04-14 02:15:31

528

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Prob. 6, Sec. 3.3, in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: How to find this limit?

Published on 14 Apr 2026 - 2:15

score 994 · Answer 15 · 2026-04-11 09:09:39

994

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How to prove that a limit is incorrect using epsilon delta definition of a limit?

Published on 11 Apr 2026 - 9:09

List Question

Calculus, how to find the value of delta in $\epsilon$-$\delta$ limit proof

Evaluating $\lim_{x\rightarrow 0}\frac{\cos(ax) - \cos(bx)}{\sin^2(x)}$

For $\{x_n\}\in X$ do we always have $\lim_{n\to\infty}\|x_n\| = 0 \quad \text{iff}\quad\lim_{n\to \infty}x_n=0?$

Prob. 2, Sec. 3.3, in INTRO. TO REAL ANALYSIS by Bartle & Sherbert: What is the limit of this sequence?

$\lim_{x\rightarrow\infty}p\left(x\right)^{\frac{1}{\ln x}}$ where $p(x)$ is a polynomial of degree $n$

Proof Verification: $\frac{(-1)^{n}n}{n+1}$ diverges

Limit of shifted indexes pairs series

Upper bound for limsup

Limits of sub sequences

If $\,\lim_{h\to 0}\frac{f(x+h)-f(x-h)}{2h}\,$ exists for every $x$, what does this imply for $f$?

Limit simplification

Computing the Limits $ (1) \lim_{n \rightarrow \infty} \frac{10^n}{n!} ~~ (2) \lim_{n \rightarrow \infty} \frac{n^n}{n!} $

How to approximate a function involving arc-tangent for a sufficiently large argument?

Prob. 6, Sec. 3.3, in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: How to find this limit?

How to prove that a limit is incorrect using epsilon delta definition of a limit?

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