Question

Using sequences to prove a limit doesn't exist?

score 2.9k · Answer 1 · 2026-03-25 11:52:56

2.9k

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Using sequences to prove a limit doesn't exist?

Published on 25 Mar 2026 - 11:52

score 883 · Answer 2 · 2026-03-29 14:59:22

883

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Prove that if $\lim_{n \to \infty} f(x_n) = f(\lim_{n \to \infty} x_n)$ for all sequences that converge to $x$, then $f$ is continuous

Published on 29 Mar 2026 - 14:59

score 108 · Answer 3 · 2026-04-11 14:32:40

108

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how can I calculate: $\lim_{n \to \infty} \frac{\frac{1}{n}-\ln(1+\frac{1}{n})}{n^{\frac{1}{n}}-1} $?

Published on 11 Apr 2026 - 14:32

score 173 · Answer 4 · 2018-01-31 21:11:53

173

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Is this a sufficient condition for the existence of a limit?

Published on 31 Jan 2018 - 21:11

score 86 · Answer 5 · 2026-04-11 07:54:07

86

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How does solving limits of a complex function differ from a normal function

Published on 11 Apr 2026 - 7:54

score 59 · Answer 6 · 2018-02-01 07:47:42

59

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Why the limit can only be $0$

Published on 01 Feb 2018 - 7:47

score 65 · Answer 7 · 2026-04-10 06:54:57

65

Views

Double limit of a net

Published on 10 Apr 2026 - 6:54

score 66 · Answer 8 · 2026-04-11 11:36:30

66

Views

How to compute this limit? Which could be an example that Cauchy's first theorem doesn't hold for infinite limits.

Published on 11 Apr 2026 - 11:36

score 179 · Answer 9 · 2026-04-08 23:13:06

179

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Calculate $\lim_{x \rightarrow 0^+} \frac{\arctan (\log (1+\sqrt x)) \sin^3(x^{3/4})}{(e^{\tan(x)}-1)(1-\sin^2(x))}$

Published on 08 Apr 2026 - 23:13

score 337 · Answer 10 · 2026-03-24 23:45:03

337

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how to find the limit $ \lim_{x\to -\infty} xe^x = 0 $ using only simple algebraic manipulation

Published on 24 Mar 2026 - 23:45

score 35 · Answer 11 · 2018-02-01 13:38:11

35

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how to prove n-th root of limit of f(x) is limit of n-th root of f(x)

Published on 01 Feb 2018 - 13:38

score 45 · Answer 12 · 2026-03-29 13:40:50

45

Views

Short proof of $d(x, A) = \lim_{n \to +\infty} d(x, A_n)$ with $(A_n)$ so that $A = \bigcup_{i=1}^n A_i$.

Published on 29 Mar 2026 - 13:40

score 373 · Answer 13 · 2026-04-09 20:19:59

373

Views

Substitution in finding limits

Published on 09 Apr 2026 - 20:19

score 52 · Answer 14 · 2018-02-01 15:48:47

52

Views

Limit Evaluation when x reach 14

Published on 01 Feb 2018 - 15:48

score 125 · Answer 15 · 2026-03-25 01:18:50

125

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Find the limit of $\lim\limits_{x\to0^+}\frac{1}{e} \frac{e- e^ \frac{\ln (1+x)}{x}}{x}$ as $x$

Published on 25 Mar 2026 - 1:18

List Question

Using sequences to prove a limit doesn't exist?

Prove that if $\lim_{n \to \infty} f(x_n) = f(\lim_{n \to \infty} x_n)$ for all sequences that converge to $x$, then $f$ is continuous

how can I calculate: $\lim_{n \to \infty} \frac{\frac{1}{n}-\ln(1+\frac{1}{n})}{n^{\frac{1}{n}}-1} $?

Is this a sufficient condition for the existence of a limit?

How does solving limits of a complex function differ from a normal function

Why the limit can only be $0$

Double limit of a net

How to compute this limit? Which could be an example that Cauchy's first theorem doesn't hold for infinite limits.

Calculate $\lim_{x \rightarrow 0^+} \frac{\arctan (\log (1+\sqrt x)) \sin^3(x^{3/4})}{(e^{\tan(x)}-1)(1-\sin^2(x))}$

how to find the limit $ \lim_{x\to -\infty} xe^x = 0 $ using only simple algebraic manipulation

how to prove n-th root of limit of f(x) is limit of n-th root of f(x)

Short proof of $d(x, A) = \lim_{n \to +\infty} d(x, A_n)$ with $(A_n)$ so that $A = \bigcup_{i=1}^n A_i$.

Substitution in finding limits

Limit Evaluation when x reach 14

Find the limit of $\lim\limits_{x\to0^+}\frac{1}{e} \frac{e- e^ \frac{\ln (1+x)}{x}}{x}$ as $x$

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