Question

Please explain the steps involved after $F(x+h)-F(x)-BAh=Bo_1(h)+o_2(\phi(h))$ in detail

score 31 · Answer 1 · 2026-03-28 11:45:10

31

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Please explain the steps involved after $F(x+h)-F(x)-BAh=Bo_1(h)+o_2(\phi(h))$ in detail

Published on 28 Mar 2026 - 11:45

score 61 · Answer 2 · 2023-04-29 22:26:04

61

Views

Continuity of $ \frac{1}{x^2} $ at $ x=1 $

Published on 29 Apr 2023 - 22:26

score 88 · Answer 3 · 2023-05-01 10:55:23

88

Views

Proof check: $f(x) = \sqrt{x}$ is continuous on $[0, \infty)$

Published on 01 May 2023 - 10:55

score 80 · Answer 4 · 2026-03-29 22:28:57

80

Views

Problem understanding quantifier for x in epsilon-delta definition of a limit

Published on 29 Mar 2026 - 22:28

score 83 · Answer 5 · 2026-03-31 03:58:15

83

Views

If $f$ is continuous on some interval and $|f|$ is uniformly continuous. Prove or disprove that $f$ is also uniformly continuous.

Published on 31 Mar 2026 - 3:58

score 23 · Answer 6 · 2023-05-09 18:26:59

23

Views

a growth condition limit estimate

Published on 09 May 2023 - 18:26

score 91 · Answer 7 · 2023-05-12 22:00:10

91

Views

Confusion regarding continuity on a subset of the domain

Published on 12 May 2023 - 22:00

score 1k · Answer 8 · 2023-05-17 07:45:53

1k

Views

Which other Real Analysis textbooks unusually advise ending delta-epsilon proofs with a cluttered $\epsilon?

Published on 17 May 2023 - 7:45

score 74 · Answer 9 · 2023-05-20 18:47:23

74

Views

$(1)\left | \sqrt[]{x} -\sqrt[]{x+\varepsilon} \right | < \frac{1}{200}, \space \space (2)\left | \sqrt[]{x} -P(x) \right | < \frac{1}{100} $

Published on 20 May 2023 - 18:47

score 71 · Answer 10 · 2023-05-30 05:05:51

71

Views

Understanding $\epsilon-\delta$ definition of continuity

Published on 30 May 2023 - 5:05

score 60 · Answer 11 · 2023-06-03 05:39:43

60

Views

Does the existence of a limit imply that a function has a maximum/minimum in that neighbourhood?

Published on 03 Jun 2023 - 5:39

score 118 · Answer 12 · 2023-06-09 23:55:27

118

Views

can we say a function $f:[a,b]\to \Bbb{R}$ is continuous at the end points?

Published on 09 Jun 2023 - 23:55

score 33 · Answer 13 · 2023-06-17 02:01:53

33

Views

Finite decimal continuity

Published on 17 Jun 2023 - 2:01

score 104 · Answer 14 · 2023-06-17 07:15:01

104

Views

Example of a limit where the Epsilon delta definition wins

Published on 17 Jun 2023 - 7:15

score 295 · Answer 15 · 2023-06-20 06:23:58

295

Views

$\epsilon$-$\delta$ proof that $\lim_{x \to 0}\frac{e^x-1}{x} = 1$ without using $\frac{d}{dx}e^x = e^x$

Published on 20 Jun 2023 - 6:23

List Question

Please explain the steps involved after $F(x+h)-F(x)-BAh=Bo_1(h)+o_2(\phi(h))$ in detail

Continuity of $ \frac{1}{x^2} $ at $ x=1 $

Proof check: $f(x) = \sqrt{x}$ is continuous on $[0, \infty)$

Problem understanding quantifier for x in epsilon-delta definition of a limit

If $f$ is continuous on some interval and $|f|$ is uniformly continuous. Prove or disprove that $f$ is also uniformly continuous.

a growth condition limit estimate

Confusion regarding continuity on a subset of the domain

Which other Real Analysis textbooks unusually advise ending delta-epsilon proofs with a cluttered $\epsilon?

$(1)\left | \sqrt[]{x} -\sqrt[]{x+\varepsilon} \right | < \frac{1}{200}, \space \space (2)\left | \sqrt[]{x} -P(x) \right | < \frac{1}{100} $

Understanding $\epsilon-\delta$ definition of continuity

Does the existence of a limit imply that a function has a maximum/minimum in that neighbourhood?

can we say a function $f:[a,b]\to \Bbb{R}$ is continuous at the end points?

Finite decimal continuity

Example of a limit where the Epsilon delta definition wins

$\epsilon$-$\delta$ proof that $\lim_{x \to 0}\frac{e^x-1}{x} = 1$ without using $\frac{d}{dx}e^x = e^x$

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