Question

Determine that the function $f(x)=\sqrt{x^2-x-6} \text{ in } x_0=3$ is continous with the $\varepsilon$-$\delta$-definition of limit/criterion

score 72 · Answer 1 · 2018-11-06 15:18:50

72

Views

Determine that the function $f(x)=\sqrt{x^2-x-6} \text{ in } x_0=3$ is continous with the $\varepsilon$-$\delta$-definition of limit/criterion

Published on 06 Nov 2018 - 15:18

score 56 · Answer 2 · 2018-11-06 16:47:29

56

Views

Mathematical analysis: Continuity of functions

Published on 06 Nov 2018 - 16:47

score 42 · Answer 3 · 2018-11-06 22:13:05

42

Views

Valid Proof on Boundedness for $f $and $f'$?

Published on 06 Nov 2018 - 22:13

score 85 · Answer 4 · 2018-11-06 23:03:44

85

Views

Determine that the function $f(x)=\dfrac{x^2+x-2}{x-1}$ is continous in $x_0=0$; $x_0\in \mathbb{R}$

Published on 06 Nov 2018 - 23:03

score 393 · Answer 5 · 2018-11-08 08:38:22

393

Views

What is a plain English explanation of "$\epsilon$-$\delta$ criterion" and how to use it for proving continuity?

Published on 08 Nov 2018 - 8:38

score 161 · Answer 6 · 2018-11-09 03:09:16

161

Views

Use the definition of limit to show that $\lim_{(x,y) \to (5,4)} 2x^2 -3y^2 = 2$.

Published on 09 Nov 2018 - 3:09

score 48 · Answer 7 · 2018-11-09 15:56:04

48

Views

Proof of limit using change of variables, help with a minor detail

Published on 09 Nov 2018 - 15:56

score 92 · Answer 8 · 2018-11-09 18:47:55

92

Views

Show that if $\pi_i \circ f$ is continuous for each i where $f$ is a function $f: \mathbb{R}^n \rightarrow{} \mathbb{R}^m$, $f$ is continuous

Published on 09 Nov 2018 - 18:47

score 152 · Answer 9 · 2018-11-09 23:55:46

152

Views

Show function is continuous given continuity of another function $\mathbb{R}^n \rightarrow{}\mathbb{R}$

Published on 09 Nov 2018 - 23:55

score 334 · Answer 10 · 2018-11-11 07:51:34

334

Views

How to prove the function $e^x$ is continous for all real numbers

Published on 11 Nov 2018 - 7:51

score 164 · Answer 11 · 2018-11-12 17:58:48

164

Views

If $f$ is continuous, then $\exists \delta > 0$ so that $\vert f(x) \vert \geq \frac{\vert f(x_0) \vert}{2} > 0$

Published on 12 Nov 2018 - 17:58

score 97 · Answer 12 · 2018-11-14 18:22:16

97

Views

If $\{a_n\} $ converges to $a$ and $\{b_n\}$ converges to $b$, and we have that $a_n < b_n$ for all $n$, is it true that $a<b$

Published on 14 Nov 2018 - 18:22

score 37 · Answer 13 · 2018-11-15 12:34:17

37

Views

What is the best that you can say about a function with given property

Published on 15 Nov 2018 - 12:34

score 58 · Answer 14 · 2018-11-16 04:40:11

58

Views

Using $\epsilon-\delta$ language to show $\lim_{x\rightarrow0}\frac{1-\cos(x)}{x}=0$.

Published on 16 Nov 2018 - 4:40

score 88 · Answer 15 · 2018-11-16 07:11:50

88

Views

Attempt at sequence proof $\frac{n+3}{n^2 -3}$ converges to $0$

Published on 16 Nov 2018 - 7:11

List Question

Determine that the function $f(x)=\sqrt{x^2-x-6} \text{ in } x_0=3$ is continous with the $\varepsilon$-$\delta$-definition of limit/criterion

Mathematical analysis: Continuity of functions

Valid Proof on Boundedness for $f $and $f'$?

Determine that the function $f(x)=\dfrac{x^2+x-2}{x-1}$ is continous in $x_0=0$; $x_0\in \mathbb{R}$

What is a plain English explanation of "$\epsilon$-$\delta$ criterion" and how to use it for proving continuity?

Use the definition of limit to show that $\lim_{(x,y) \to (5,4)} 2x^2 -3y^2 = 2$.

Proof of limit using change of variables, help with a minor detail

Show that if $\pi_i \circ f$ is continuous for each i where $f$ is a function $f: \mathbb{R}^n \rightarrow{} \mathbb{R}^m$, $f$ is continuous

Show function is continuous given continuity of another function $\mathbb{R}^n \rightarrow{}\mathbb{R}$

How to prove the function $e^x$ is continous for all real numbers

If $f$ is continuous, then $\exists \delta > 0$ so that $\vert f(x) \vert \geq \frac{\vert f(x_0) \vert}{2} > 0$

If $\{a_n\} $ converges to $a$ and $\{b_n\}$ converges to $b$, and we have that $a_n < b_n$ for all $n$, is it true that $a<b$

What is the best that you can say about a function with given property

Using $\epsilon-\delta$ language to show $\lim_{x\rightarrow0}\frac{1-\cos(x)}{x}=0$.

Attempt at sequence proof $\frac{n+3}{n^2 -3}$ converges to $0$

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