Question

How does $ax^2 − 2x^2 − a^2x − 2a^2 $ result in $ |ax||x − a| + 2|x^2 − a^2 | $ by the triangle inequality?

score 34 · Answer 1 · 2019-12-09 03:53:49

34

Views

How does $ax^2 − 2x^2 − a^2x − 2a^2 $ result in $ |ax||x − a| + 2|x^2 − a^2 | $ by the triangle inequality?

Published on 09 Dec 2019 - 3:53

score 44 · Answer 2 · 2019-12-10 19:59:43

44

Views

What is wrong with my approach for finding a suitable $\delta$ for an arbitrary $\epsilon$?

Published on 10 Dec 2019 - 19:59

score 67 · Answer 3 · 2019-12-10 20:32:55

67

Views

Show that function $f(x) = 11\|x\|^{22}$ is continuous

Published on 10 Dec 2019 - 20:32

score 74 · Answer 4 · 2019-12-11 19:32:46

74

Views

Let $f(0) = -1, f(x+y) \leq -f(x)f(y)$, show that $f \text{ continuous in } \mathbb{R} \iff f \text{ continuous in } 0$

Published on 11 Dec 2019 - 19:32

score 56 · Answer 5 · 2019-12-11 21:42:43

56

Views

Is this delta epsilon proof ok? (single variable)

Published on 11 Dec 2019 - 21:42

score 44 · Answer 6 · 2019-12-13 00:30:18

44

Views

Contradiction on limit argument

Published on 13 Dec 2019 - 0:30

score 127 · Answer 7 · 2019-12-14 09:53:53

127

Views

Prove the limit of $\lim_{x \to 0^+}e^{\frac{1}{x}}$ and $\lim_{x \to 0^-}e^{\frac{1}{x}}$

Published on 14 Dec 2019 - 9:53

score 1.3k · Answer 8 · 2019-12-15 22:58:08

1.3k

Views

Why do we choose $|l - m| \over 2$ as $\epsilon$ in this proof of the Uniqueness of a Limit?

Published on 15 Dec 2019 - 22:58

score 124 · Answer 9 · 2019-12-16 19:31:34

124

Views

Question about epsilon-delta proofs in general

Published on 16 Dec 2019 - 19:31

score 1k · Answer 10 · 2019-12-17 10:58:25

1k

Views

Proving a limit exists using Squeeze Theorem

Published on 17 Dec 2019 - 10:58

score 46 · Answer 11 · 2026-03-26 20:44:02

46

Views

Show the uniform continuity of $\frac{1}{1+x^4}$ per Lipschitz-continuity or $\varepsilon - \delta$-proof

Published on 26 Mar 2026 - 20:44

score 308 · Answer 12 · 2019-12-21 22:37:14

308

Views

Using $\epsilon-\delta$ arguments, find the limit of $(e^{xy} -1)/y$ when $(x,y)\to(0,0)$

Published on 21 Dec 2019 - 22:37

score 91 · Answer 13 · 2019-12-22 12:44:09

91

Views

Any tips for $\varepsilon(-\delta)$-proofs?

Published on 22 Dec 2019 - 12:44

score 68 · Answer 14 · 2019-12-24 23:53:12

68

Views

Proving $\lim_{(x,y)\to(0,0)} \frac{\cos(xy)-1}{x}=0$ using $(\epsilon,\delta)$-arguments

Published on 24 Dec 2019 - 23:53

score 447 · Answer 15 · 2026-03-29 05:42:39

447

Views

$\sin(2\pi x[x])$ is continuous on $\mathbb R$

Published on 29 Mar 2026 - 5:42

List Question

How does $ax^2 − 2x^2 − a^2x − 2a^2 $ result in $ |ax||x − a| + 2|x^2 − a^2 | $ by the triangle inequality?

What is wrong with my approach for finding a suitable $\delta$ for an arbitrary $\epsilon$?

Show that function $f(x) = 11\|x\|^{22}$ is continuous

Let $f(0) = -1, f(x+y) \leq -f(x)f(y)$, show that $f \text{ continuous in } \mathbb{R} \iff f \text{ continuous in } 0$

Is this delta epsilon proof ok? (single variable)

Contradiction on limit argument

Prove the limit of $\lim_{x \to 0^+}e^{\frac{1}{x}}$ and $\lim_{x \to 0^-}e^{\frac{1}{x}}$

Why do we choose $|l - m| \over 2$ as $\epsilon$ in this proof of the Uniqueness of a Limit?

Question about epsilon-delta proofs in general

Proving a limit exists using Squeeze Theorem

Show the uniform continuity of $\frac{1}{1+x^4}$ per Lipschitz-continuity or $\varepsilon - \delta$-proof

Using $\epsilon-\delta$ arguments, find the limit of $(e^{xy} -1)/y$ when $(x,y)\to(0,0)$

Any tips for $\varepsilon(-\delta)$-proofs?

Proving $\lim_{(x,y)\to(0,0)} \frac{\cos(xy)-1}{x}=0$ using $(\epsilon,\delta)$-arguments

$\sin(2\pi x[x])$ is continuous on $\mathbb R$

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