Question

Using a positive constant C in proving a limit

score 506 · Answer 1 · 2018-03-26 13:35:53

506

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Using a positive constant C in proving a limit

Published on 26 Mar 2018 - 13:35

score 56 · Answer 2 · 2018-03-27 19:09:42

56

Views

Given $J \subseteq I \subseteq \mathbb{R}$ open intervals, prove $\lim_{x \rightarrow c}f(x)=\lim_{x \rightarrow c}f\mid_J(x)$

Published on 27 Mar 2018 - 19:09

score 159 · Answer 3 · 2018-03-27 21:10:07

159

Views

(Another) Multivariable delta-epsilon proof

Published on 27 Mar 2018 - 21:10

score 404 · Answer 4 · 2018-03-28 00:56:22

404

Views

Showing that the projection map $\mathbb{R^2}\to\mathbb{R}, (x,y)\mapsto x$ is continuous

Published on 28 Mar 2018 - 0:56

score 119 · Answer 5 · 2018-03-28 07:08:37

119

Views

Formal Definition Of Limit with Sequence

Published on 28 Mar 2018 - 7:08

score 1.9k · Answer 6 · 2018-03-28 08:42:27

1.9k

Views

How to prove that $x^n$ is continuous on $(0, \infty)$

Published on 28 Mar 2018 - 8:42

score 311 · Answer 7 · 2018-03-29 06:36:57

311

Views

Prove that $f'(x) = \lim_{h\to 0^+ \\k\to 0^+} \frac{f(x+h) - f(x-k)}{h+k}$

Published on 29 Mar 2018 - 6:36

score 158 · Answer 8 · 2018-03-29 17:04:24

158

Views

Find a $\delta$ such that $\lvert \sqrt{x} - 1 \rvert<\varepsilon$ for all $x$ satisfying $0<\lvert x-1 \rvert <\delta$

Published on 29 Mar 2018 - 17:04

score 62 · Answer 9 · 2018-03-31 03:54:35

62

Views

Proving a function is continuous using $\varepsilon -\delta$ definition

Published on 31 Mar 2018 - 3:54

score 1.4k · Answer 10 · 2018-03-31 08:35:45

1.4k

Views

Studying uniform continuity on a multivariable function.

Published on 31 Mar 2018 - 8:35

score 2.5k · Answer 11 · 2018-03-31 10:31:28

2.5k

Views

Proving limits for fractions using epsilon-delta definition

Published on 31 Mar 2018 - 10:31

score 37 · Answer 12 · 2018-03-31 11:41:14

37

Views

Need help proving a limit using the definition of a limit.

Published on 31 Mar 2018 - 11:41

score 141 · Answer 13 · 2018-04-01 18:19:19

141

Views

if $\lim_{x \to 0} \frac{f(x)}{x} = l$ and $b\neq0$, then $\lim_{x \to o} \frac{f(bx)}{x} = bl$

Published on 01 Apr 2018 - 18:19

score 655 · Answer 14 · 2018-04-01 18:56:20

655

Views

Limit of a bounded function is bounded

Published on 01 Apr 2018 - 18:56

score 31 · Answer 15 · 2018-04-01 22:33:31

31

Views

Let $p$ be a point in $X$ at which $f(p) \gt 0$ Show there is some positive number $r$ such that $f(q) \gt 0$ for all q in $B_r(p)$

Published on 01 Apr 2018 - 22:33

List Question

Using a positive constant C in proving a limit

Given $J \subseteq I \subseteq \mathbb{R}$ open intervals, prove $\lim_{x \rightarrow c}f(x)=\lim_{x \rightarrow c}f\mid_J(x)$

(Another) Multivariable delta-epsilon proof

Showing that the projection map $\mathbb{R^2}\to\mathbb{R}, (x,y)\mapsto x$ is continuous

Formal Definition Of Limit with Sequence

How to prove that $x^n$ is continuous on $(0, \infty)$

Prove that $f'(x) = \lim_{h\to 0^+ \\k\to 0^+} \frac{f(x+h) - f(x-k)}{h+k}$

Find a $\delta$ such that $\lvert \sqrt{x} - 1 \rvert<\varepsilon$ for all $x$ satisfying $0<\lvert x-1 \rvert <\delta$

Proving a function is continuous using $\varepsilon -\delta$ definition

Studying uniform continuity on a multivariable function.

Proving limits for fractions using epsilon-delta definition

Need help proving a limit using the definition of a limit.

if $\lim_{x \to 0} \frac{f(x)}{x} = l$ and $b\neq0$, then $\lim_{x \to o} \frac{f(bx)}{x} = bl$

Limit of a bounded function is bounded

Let $p$ be a point in $X$ at which $f(p) \gt 0$ Show there is some positive number $r$ such that $f(q) \gt 0$ for all q in $B_r(p)$

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