Question

Is it possible that $\delta$ is always equal to $\varepsilon$ when the function of given limit has identical roots?

score 40 · Answer 1 · 2019-09-24 07:55:46

40

Views

Is it possible that $\delta$ is always equal to $\varepsilon$ when the function of given limit has identical roots?

Published on 24 Sep 2019 - 7:55

score 90 · Answer 2 · 2019-09-24 19:02:45

90

Views

Limit And Continuity of $f(x) = \left\{\begin{matrix} x^{2} ; x \in \mathbb{Q} & \\ 0 ; x \not\in \mathbb{Q} & \end{matrix}\right.$

Published on 24 Sep 2019 - 19:02

score 718 · Answer 3 · 2019-09-27 00:12:30

718

Views

A (possibly) difficult epsilon-delta proof

Published on 27 Sep 2019 - 0:12

score 181 · Answer 4 · 2019-09-27 20:24:30

181

Views

epsilon-delta proof involving a fractional exponent

Published on 27 Sep 2019 - 20:24

score 311 · Answer 5 · 2019-09-29 05:20:16

311

Views

How do I prove the limit $\frac{\sin(xy)}{\sqrt{x^2 + y^2}}$ as (x, y) approaches (0, 0) using $\epsilon - \delta$

Published on 29 Sep 2019 - 5:20

score 78 · Answer 6 · 2019-10-01 14:01:48

78

Views

Let $\{x_n\}_{n=1}^\infty$ be a convergent sequence in R with limit x. Show that $\lim_{n\to\infty} 1/n \sum_{k=1}^{n} x_k = x$

Published on 01 Oct 2019 - 14:01

score 1.5k · Answer 7 · 2014-03-12 04:09:45

1.5k

Views

Show $\lim\limits_{(x,y)\to(0,0)} \frac{xy}{\sqrt{x^2+y^2}}=0$ using Delta Epsilon Proof

Published on 12 Mar 2014 - 4:09

score 262 · Answer 8 · 2014-03-14 06:38:52

262

Views

Epsilon-Delta More Confusion

Published on 14 Mar 2014 - 6:38

score 1.6k · Answer 9 · 2014-03-16 23:11:57

1.6k

Views

I need help understanding the formal definition of a limit

Published on 16 Mar 2014 - 23:11

score 11.3k · Answer 10 · 2014-04-12 21:42:11

11.3k

Views

Help with epsilon-delta proof that 1/(x^2) is continuous at a point.

Published on 12 Apr 2014 - 21:42

score 844 · Answer 11 · 2014-04-16 08:20:15

844

Views

$\epsilon - N$ proof confirmation.

Published on 16 Apr 2014 - 8:20

score 1k · Answer 12 · 2014-04-19 09:50:02

1k

Views

Find out if $f$ differentiable, continuous and have partial derivatives - or if it does not. Using definitions.

Published on 19 Apr 2014 - 9:50

score 257 · Answer 13 · 2014-04-21 19:30:14

257

Views

Limit of $f(x)=\frac{x}{1+\sin^2x}$ as $x\to0$ and proof

Published on 21 Apr 2014 - 19:30

score 1.1k · Answer 14 · 2014-04-25 22:49:19

1.1k

Views

Spivak Ch 11 Theorem 7

Published on 25 Apr 2014 - 22:49

score 1.1k · Answer 15 · 2014-04-29 14:26:01

1.1k

Views

Proving that $f(x) = e^{-x}$ is not uniformly continuous on $\mathbb{R}$

Published on 29 Apr 2014 - 14:26

List Question

Is it possible that $\delta$ is always equal to $\varepsilon$ when the function of given limit has identical roots?

Limit And Continuity of $f(x) = \left\{\begin{matrix} x^{2} ; x \in \mathbb{Q} & \\ 0 ; x \not\in \mathbb{Q} & \end{matrix}\right.$

A (possibly) difficult epsilon-delta proof

epsilon-delta proof involving a fractional exponent

How do I prove the limit $\frac{\sin(xy)}{\sqrt{x^2 + y^2}}$ as (x, y) approaches (0, 0) using $\epsilon - \delta$

Let $\{x_n\}_{n=1}^\infty$ be a convergent sequence in R with limit x. Show that $\lim_{n\to\infty} 1/n \sum_{k=1}^{n} x_k = x$

Show $\lim\limits_{(x,y)\to(0,0)} \frac{xy}{\sqrt{x^2+y^2}}=0$ using Delta Epsilon Proof

Epsilon-Delta More Confusion

I need help understanding the formal definition of a limit

Help with epsilon-delta proof that 1/(x^2) is continuous at a point.

$\epsilon - N$ proof confirmation.

Find out if $f$ differentiable, continuous and have partial derivatives - or if it does not. Using definitions.

Limit of $f(x)=\frac{x}{1+\sin^2x}$ as $x\to0$ and proof

Spivak Ch 11 Theorem 7

Proving that $f(x) = e^{-x}$ is not uniformly continuous on $\mathbb{R}$

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