Question

Prove that the function $f(z) = \frac{1}{1-z}$ is not uniformly continuous on $(-1,1)$

score 1.4k · Answer 1 · 2026-04-01 23:32:22

1.4k

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Prove that the function $f(z) = \frac{1}{1-z}$ is not uniformly continuous on $(-1,1)$

Published on 01 Apr 2026 - 23:32

score 1.2k · Answer 2 · 2016-02-09 23:57:53

1.2k

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Find $\lim x^2+2x-1=7$ as $x \rightarrow 2$ using epsilon-delta proof.

Published on 09 Feb 2016 - 23:57

score 62 · Answer 3 · 2016-02-10 00:21:24

62

Views

$\lim \frac{\sqrt{x}-1}{x-1}=\frac{1}{2}$ as $x \rightarrow 1$ Epsilon-Delta proof help.

Published on 10 Feb 2016 - 0:21

score 533 · Answer 4 · 2016-02-10 10:40:40

533

Views

Prove that $\lim_{x\rightarrow \infty} \frac{x^2 - 1}{x^2 + 1} = 1$ using definition of limit.

Published on 10 Feb 2016 - 10:40

score 1k · Answer 5 · 2026-03-29 10:59:57

1k

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Strictly monotone functions and continuity

Published on 29 Mar 2026 - 10:59

score 244 · Answer 6 · 2016-02-13 01:59:20

244

Views

Proving that if the sequence $\{s_n-L\}$ converges to zero, then a sequence $\{s_n\}$ converges to a limit $L$

Published on 13 Feb 2016 - 1:59

score 72 · Answer 7 · 2016-02-13 02:28:14

72

Views

Show that a sequence $\{s_n\}$ converges to $L$ if and only if the sequence $\{-s_n\}$ converges to $-L$.

Published on 13 Feb 2016 - 2:28

score 599 · Answer 8 · 2016-02-13 07:01:13

599

Views

prove limit of exponential function without concept of logarithm

Published on 13 Feb 2016 - 7:01

score 355 · Answer 9 · 2016-02-13 19:29:33

355

Views

The limit of $\frac{1}{z}$ in complex number

Published on 13 Feb 2016 - 19:29

score 4.4k · Answer 10 · 2016-02-21 17:02:26

4.4k

Views

Show that the complex function f is continuous at the given point

Published on 21 Feb 2016 - 17:02

score 33 · Answer 11 · 2016-02-21 19:24:50

33

Views

Is the axiom of countable choice needed for the proof of this special case of equivalence of limit definitions?

Published on 21 Feb 2016 - 19:24

score 111 · Answer 12 · 2016-02-22 03:51:19

111

Views

Proving a particular limit doesn't exist ($\varepsilon$-$\delta$).

Published on 22 Feb 2016 - 3:51

score 313 · Answer 13 · 2016-02-23 18:52:36

313

Views

Show that $f'(0)= \lim_{\Delta x \to 0}\frac{f(\Delta x)-1}{\Delta x} = 1$

Published on 23 Feb 2016 - 18:52

score 23 · Answer 14 · 2016-02-27 12:41:34

23

Views

Show that there is real $r$ such that for every real $x$ we have $l\cdot f(x)>0$

Published on 27 Feb 2016 - 12:41

score 46 · Answer 15 · 2016-02-27 19:02:27

46

Views

Comparing $\delta$ to $x-a$ in limit as $x$ approaches $a$

Published on 27 Feb 2016 - 19:02

List Question

Prove that the function $f(z) = \frac{1}{1-z}$ is not uniformly continuous on $(-1,1)$

Find $\lim x^2+2x-1=7$ as $x \rightarrow 2$ using epsilon-delta proof.

$\lim \frac{\sqrt{x}-1}{x-1}=\frac{1}{2}$ as $x \rightarrow 1$ Epsilon-Delta proof help.

Prove that $\lim_{x\rightarrow \infty} \frac{x^2 - 1}{x^2 + 1} = 1$ using definition of limit.

Strictly monotone functions and continuity

Proving that if the sequence $\{s_n-L\}$ converges to zero, then a sequence $\{s_n\}$ converges to a limit $L$

Show that a sequence $\{s_n\}$ converges to $L$ if and only if the sequence $\{-s_n\}$ converges to $-L$.

prove limit of exponential function without concept of logarithm

The limit of $\frac{1}{z}$ in complex number

Show that the complex function f is continuous at the given point

Is the axiom of countable choice needed for the proof of this special case of equivalence of limit definitions?

Proving a particular limit doesn't exist ($\varepsilon$-$\delta$).

Show that $f'(0)= \lim_{\Delta x \to 0}\frac{f(\Delta x)-1}{\Delta x} = 1$

Show that there is real $r$ such that for every real $x$ we have $l\cdot f(x)>0$

Comparing $\delta$ to $x-a$ in limit as $x$ approaches $a$

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