Question

Use the definition of limit to establish $ \lim_{x\rightarrow 2} \frac{1}{1-x}= -1$

score 42 · Answer 1 · 2016-12-05 02:27:36

42

Views

Use the definition of limit to establish $ \lim_{x\rightarrow 2} \frac{1}{1-x}= -1$

Published on 05 Dec 2016 - 2:27

score 474 · Answer 2 · 2016-12-06 00:41:00

474

Views

Proving limit using precise limit definition

Published on 06 Dec 2016 - 0:41

score 1.1k · Answer 3 · 2016-12-06 22:44:36

1.1k

Views

Proving that a limit of a piecewise constant function does not exist using $\epsilon$-$\delta$

Published on 06 Dec 2016 - 22:44

score 100 · Answer 4 · 2016-12-07 05:28:13

100

Views

If $f(x) \leq M$ for all $x \in\mathbb{R}$ and $\lim_{x\to c} f(x) = L$, show that $L \leq M$.

Published on 07 Dec 2016 - 5:28

score 346 · Answer 5 · 2016-12-07 11:36:55

346

Views

In epsilon delta method, is this possible?

Published on 07 Dec 2016 - 11:36

score 58 · Answer 6 · 2016-12-07 14:24:32

What are the necessary conditions for $\delta =\min \left\{ f^{-1}\left( x_{0}-\varepsilon \right) ,f^{-1}\left( x_{0}+\varepsilon \right) \right\}$?

score 27 · Answer 7 · 2026-03-26 21:27:37

27

Views

How to find an upper bound for an asymptotic relation $\frac{\epsilon}{\delta^{2}}$ using that $\delta \ll \epsilon^{2}$?

Published on 26 Mar 2026 - 21:27

score 35 · Answer 8 · 2016-12-08 11:41:37

35

Views

A problem related to continuity

Published on 08 Dec 2016 - 11:41

score 311 · Answer 9 · 2016-12-09 23:26:43

311

Views

lim 1/(x-3) (epsilon delta)

Published on 09 Dec 2016 - 23:26

score 90 · Answer 10 · 2016-12-10 20:33:55

90

Views

Prove $\lim_{x\to2} \sqrt{4x-x^2} = 2$ by definition with $\epsilon, \delta$

Published on 10 Dec 2016 - 20:33

score 1k · Answer 11 · 2016-12-12 01:48:58

1k

Views

Proving a sequence converges $\epsilon-N$

Published on 12 Dec 2016 - 1:48

score 3.8k · Answer 12 · 2026-03-30 10:39:27

3.8k

Views

Is $f(x)=\frac{1}{x^2+1}$ uniformly continuous on $\mathbb{R}$?

Published on 30 Mar 2026 - 10:39

score 340 · Answer 13 · 2016-12-13 22:37:50

340

Views

If $\lvert f(x)-f(y) \rvert \le \lvert x-y \rvert ^2$ for all $x$ and $y$ in $\mathbb{R}$ then $f$ is a constant function

Published on 13 Dec 2016 - 22:37

score 43 · Answer 14 · 2016-12-14 13:34:02

43

Views

Use the definition of a limit to prove $\lim_{x\rightarrow 0}(x^2-x)\sin\left ( \frac{1}{x} \right )=0$

Published on 14 Dec 2016 - 13:34

score 527 · Answer 15 · 2016-12-17 21:50:56

527

Views

Prove the continuity of Power Functions

Published on 17 Dec 2016 - 21:50

List Question

Use the definition of limit to establish $ \lim_{x\rightarrow 2} \frac{1}{1-x}= -1$

Proving limit using precise limit definition

Proving that a limit of a piecewise constant function does not exist using $\epsilon$-$\delta$

If $f(x) \leq M$ for all $x \in\mathbb{R}$ and $\lim_{x\to c} f(x) = L$, show that $L \leq M$.

In epsilon delta method, is this possible?

What are the necessary conditions for $\delta =\min \left\{ f^{-1}\left( x_{0}-\varepsilon \right) ,f^{-1}\left( x_{0}+\varepsilon \right) \right\}$?

How to find an upper bound for an asymptotic relation $\frac{\epsilon}{\delta^{2}}$ using that $\delta \ll \epsilon^{2}$?

A problem related to continuity

lim 1/(x-3) (epsilon delta)

Prove $\lim_{x\to2} \sqrt{4x-x^2} = 2$ by definition with $\epsilon, \delta$

Proving a sequence converges $\epsilon-N$

Is $f(x)=\frac{1}{x^2+1}$ uniformly continuous on $\mathbb{R}$?

If $\lvert f(x)-f(y) \rvert \le \lvert x-y \rvert ^2$ for all $x$ and $y$ in $\mathbb{R}$ then $f$ is a constant function

Use the definition of a limit to prove $\lim_{x\rightarrow 0}(x^2-x)\sin\left ( \frac{1}{x} \right )=0$

Prove the continuity of Power Functions

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