Question

$f(x+y)=f(x)+f(y)\;\land\;\lim_{x\rightarrow 0}f(x)=f(0)$. Prove $f(x)$ is continuous at all $a$. (Question about a particular step)

score 44 · Answer 1 · 2026-03-28 01:08:33

44

Views

$f(x+y)=f(x)+f(y)\;\land\;\lim_{x\rightarrow 0}f(x)=f(0)$. Prove $f(x)$ is continuous at all $a$. (Question about a particular step)

Published on 28 Mar 2026 - 1:08

score 492 · Answer 2 · 2020-02-17 00:37:00

492

Views

Prove that a sequence that contains subsequences that converges to every unit fraction contains a subsequence that converges to $0$.

Published on 17 Feb 2020 - 0:37

score 2k · Answer 3 · 2020-02-20 22:00:35

2k

Views

In the epsilon-delta definition, what is wrong if I said: "given delta, there exists an epsilon"?

Published on 20 Feb 2020 - 22:00

score 119 · Answer 4 · 2020-02-22 15:14:33

119

Views

Show that $\lim\limits_{x \to 2} \bigg( 2^{x} \bigg)=4$ using epsilon-delta

Published on 22 Feb 2020 - 15:14

score 779 · Answer 5 · 2026-03-26 21:07:19

779

Views

Equilibrium stability for ODE using epsilon-delta proof.

Published on 26 Mar 2026 - 21:07

score 68 · Answer 6 · 2020-02-23 01:58:32

68

Views

Proof of a limit as $x\to 0$

Published on 23 Feb 2020 - 1:58

score 44 · Answer 7 · 2020-02-23 14:58:46

44

Views

Question about the Epsilon-Delta definition of a limit

Published on 23 Feb 2020 - 14:58

score 324 · Answer 8 · 2020-02-24 13:17:50

324

Views

Prove that $\lim_{x\to x_0} x^2 = x_0^2$

Published on 24 Feb 2020 - 13:17

score 90 · Answer 9 · 2020-02-24 16:59:08

90

Views

Prove that $\lim_{x\to 3} (2x^2-5)=13$

Published on 24 Feb 2020 - 16:59

score 956 · Answer 10 · 2020-02-29 21:21:58

956

Views

Proving that $\lim_{(x,y)\rightarrow{}(0,0)}f(x,y)=0$ doesn't hold using the definition.

Published on 29 Feb 2020 - 21:21

score 52 · Answer 11 · 2020-03-04 09:04:57

52

Views

Prove the following sequence converges to 2:

Published on 04 Mar 2020 - 9:04

score 368 · Answer 12 · 2020-03-04 23:11:33

368

Views

Show that $f(x)=1/x$ is a continuous function for any $x\neq 0$

Published on 04 Mar 2020 - 23:11

score 52 · Answer 13 · 2020-03-05 03:17:00

52

Views

How can I use epsilon-delta to solve this problem?

Published on 05 Mar 2020 - 3:17

score 29 · Answer 14 · 2020-03-06 20:40:25

29

Views

$\lim\limits_{x\to a} f(x)=L$ then $\lim\limits_{x\to (a+c)} f(x-c)=L$ by using $\epsilon-\delta$ definition.

Published on 06 Mar 2020 - 20:40

score 117 · Answer 15 · 2020-03-08 07:10:20

117

Views

Using the X - Definition To Solve Limits

Published on 08 Mar 2020 - 7:10

List Question

$f(x+y)=f(x)+f(y)\;\land\;\lim_{x\rightarrow 0}f(x)=f(0)$. Prove $f(x)$ is continuous at all $a$. (Question about a particular step)

Prove that a sequence that contains subsequences that converges to every unit fraction contains a subsequence that converges to $0$.

In the epsilon-delta definition, what is wrong if I said: "given delta, there exists an epsilon"?

Show that $\lim\limits_{x \to 2} \bigg( 2^{x} \bigg)=4$ using epsilon-delta

Equilibrium stability for ODE using epsilon-delta proof.

Proof of a limit as $x\to 0$

Question about the Epsilon-Delta definition of a limit

Prove that $\lim_{x\to x_0} x^2 = x_0^2$

Prove that $\lim_{x\to 3} (2x^2-5)=13$

Proving that $\lim_{(x,y)\rightarrow{}(0,0)}f(x,y)=0$ doesn't hold using the definition.

Prove the following sequence converges to 2:

Show that $f(x)=1/x$ is a continuous function for any $x\neq 0$

How can I use epsilon-delta to solve this problem?

$\lim\limits_{x\to a} f(x)=L$ then $\lim\limits_{x\to (a+c)} f(x-c)=L$ by using $\epsilon-\delta$ definition.

Using the X - Definition To Solve Limits

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