Question

Very specific quibble re: proving that $g(x)=\sqrt[3]{x}$ is continuous at $c \neq 0$ using $\epsilon-\delta$ arguments

score 61 · Answer 1 · 2019-07-14 02:37:37

61

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Very specific quibble re: proving that $g(x)=\sqrt[3]{x}$ is continuous at $c \neq 0$ using $\epsilon-\delta$ arguments

Published on 14 Jul 2019 - 2:37

score 59 · Answer 2 · 2026-03-25 21:54:05

59

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Do the following extra highlighted words in the $\epsilon-\delta$ definition of limit prevent us from concluding that the limit exists? Why? Why not?

Published on 25 Mar 2026 - 21:54

score 241 · Answer 3 · 2026-03-26 19:00:38

241

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Proof that the harmonic function defined by the Poisson integral is continuous on the boundary of a ball.

Published on 26 Mar 2026 - 19:00

score 222 · Answer 4 · 2019-07-20 17:00:13

222

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Epsilon-Delta-Definition: How to prove $f(x)=x\cdot \sin\left(\frac{1}{x}\right)$ is continuous in $x_0=0$

Published on 20 Jul 2019 - 17:00

score 131 · Answer 5 · 2019-07-22 08:32:10

131

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Epsilon - N Proof of a diverging sequence to infinity

Published on 22 Jul 2019 - 8:32

score 114 · Answer 6 · 2019-07-22 21:42:40

114

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Show that for any $a \ne 0$, $f(x)=1/x$ approaches $1/a$ as $x$ approaches $a$.

Published on 22 Jul 2019 - 21:42

score 66 · Answer 7 · 2019-07-23 00:15:52

66

Views

Proving divergence of the fraction of the square root - without using proof by contradiction

Published on 23 Jul 2019 - 0:15

score 150 · Answer 8 · 2019-07-28 06:46:28

150

Views

Proof by epsilon-delta of $\lim \limits_{x \to 1} 3x^2+1=4$

Published on 28 Jul 2019 - 6:46

score 57 · Answer 9 · 2019-07-29 20:34:28

57

Views

For $f(x)=\sin(\frac{1}{x})$, how would $\delta>0$ change after switching the interval $(0,1)$ to $(0,1]$?

Published on 29 Jul 2019 - 20:34

score 81 · Answer 10 · 2019-07-30 04:52:40

81

Views

How to evaluate a multi-variable limit considering $f : \mathbb R^2 \to \mathbb R$?

Published on 30 Jul 2019 - 4:52

score 101 · Answer 11 · 2019-07-31 18:01:42

101

Views

Proving continuity of the following piecewise function

Published on 31 Jul 2019 - 18:01

score 65 · Answer 12 · 2019-08-01 08:06:46

65

Views

Prove that $\lim_{n\to\infty} \frac{1+\sin{(n)}}{n} = 0$.

Published on 01 Aug 2019 - 8:06

score 111 · Answer 13 · 2019-08-01 21:22:35

111

Views

Is this $\epsilon-\delta$ proof correct?

Published on 01 Aug 2019 - 21:22

score 144 · Answer 14 · 2019-08-02 16:46:12

144

Views

Show that $\lim_{(x,y)\to (0,0)} {xy\over \sqrt{x^2+y^2}}$ exists

Published on 02 Aug 2019 - 16:46

score 1k · Answer 15 · 2019-08-03 19:23:09

1k

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Proving a Limit Involving a Square Root Function Using Epsilon and Delta

Published on 03 Aug 2019 - 19:23

List Question

Very specific quibble re: proving that $g(x)=\sqrt[3]{x}$ is continuous at $c \neq 0$ using $\epsilon-\delta$ arguments

Do the following extra highlighted words in the $\epsilon-\delta$ definition of limit prevent us from concluding that the limit exists? Why? Why not?

Proof that the harmonic function defined by the Poisson integral is continuous on the boundary of a ball.

Epsilon-Delta-Definition: How to prove $f(x)=x\cdot \sin\left(\frac{1}{x}\right)$ is continuous in $x_0=0$

Epsilon - N Proof of a diverging sequence to infinity

Show that for any $a \ne 0$, $f(x)=1/x$ approaches $1/a$ as $x$ approaches $a$.

Proving divergence of the fraction of the square root - without using proof by contradiction

Proof by epsilon-delta of $\lim \limits_{x \to 1} 3x^2+1=4$

For $f(x)=\sin(\frac{1}{x})$, how would $\delta>0$ change after switching the interval $(0,1)$ to $(0,1]$?

How to evaluate a multi-variable limit considering $f : \mathbb R^2 \to \mathbb R$?

Proving continuity of the following piecewise function

Prove that $\lim_{n\to\infty} \frac{1+\sin{(n)}}{n} = 0$.

Is this $\epsilon-\delta$ proof correct?

Show that $\lim_{(x,y)\to (0,0)} {xy\over \sqrt{x^2+y^2}}$ exists

Proving a Limit Involving a Square Root Function Using Epsilon and Delta

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