Question

Is this statement equivalent to the definition of the limit?

score 89 · Answer 1 · 2021-06-02 07:07:56

89

Views

Is this statement equivalent to the definition of the limit?

Published on 02 Jun 2021 - 7:07

score 170 · Answer 2 · 2021-06-04 20:30:11

170

Views

How to solve $\epsilon$−$\delta$ limit with square roots of negative values

Published on 04 Jun 2021 - 20:30

score 47 · Answer 3 · 2021-06-05 12:43:37

47

Views

Can we strictly prove that smaller delta will still satisfy epsilon in the proof of continuity?

Published on 05 Jun 2021 - 12:43

score 754 · Answer 4 · 2021-06-06 20:40:34

754

Views

Prove that $f(x)=\begin{cases}0, & x\notin \mathbb{Q}\\ \frac{1}{q}, & x=\frac{p}{q} \text{ in lowest terms}\\ \end{cases}$ is integrable on $[0,1]$.

Published on 06 Jun 2021 - 20:40

score 345 · Answer 5 · 2021-06-09 00:40:45

345

Views

Proof of the limit of product of sequences

Published on 09 Jun 2021 - 0:40

score 104 · Answer 6 · 2021-06-10 07:17:11

104

Views

Why we choose $\epsilon_1 <\min \left(1, \frac{\varepsilon}{2 M}\right)$ and $\epsilon_2<\min \left(1, \frac{\varepsilon}{2 (|a|+1)}\right)$

Published on 10 Jun 2021 - 7:17

score 79 · Answer 7 · 2021-06-10 19:39:07

79

Views

Use the definition of a limit to prove the following: $\lim\limits_{x\to0}\frac{\cos x}{x^{2}}=\infty$

Published on 10 Jun 2021 - 19:39

score 113 · Answer 8 · 2021-06-11 07:33:11

113

Views

Use the definition of a limit to prove the following: $\lim_{x\to4}\frac{x-2}{\sqrt{x}+2}=\frac{1}{2}$

Published on 11 Jun 2021 - 7:33

score 275 · Answer 9 · 2021-06-11 21:18:22

275

Views

Necessity of selecting value for $\delta$ in $\epsilon$-$\delta$ proofs

Published on 11 Jun 2021 - 21:18

score 105 · Answer 10 · 2021-06-12 03:37:23

105

Views

How can I prove that $\lim _{x\to 0}\left(\frac{1}{f\left(x\right)}\right)=\frac{1}{L}$ using the $ε-δ $ argument

Published on 12 Jun 2021 - 3:37

score 244 · Answer 11 · 2021-06-12 23:12:14

244

Views

Proof writing: $\varepsilon$-$\delta$ proof of the product rule for limits --- any tips for cleaning this up?

Published on 12 Jun 2021 - 23:12

score 176 · Answer 12 · 2021-06-14 15:05:05

176

Views

When proving $\lim\limits_{x\to2}x^2=4$, can $\delta$ contain $x$?

Published on 14 Jun 2021 - 15:05

score 69 · Answer 13 · 2021-06-15 21:00:29

69

Views

Prove a limit with $\varepsilon$-$\delta$ definition:

Published on 15 Jun 2021 - 21:00

score 160 · Answer 14 · 2021-06-16 08:16:02

160

Views

Proof of a quotient when a limit approaches infinity

Published on 16 Jun 2021 - 8:16

score 292 · Answer 15 · 2026-04-07 00:39:19

292

Views

$ x \sin(\frac{1}{x}) $ Riemann integrable on [-1,1]?

Published on 07 Apr 2026 - 0:39

List Question

Is this statement equivalent to the definition of the limit?

How to solve $\epsilon$−$\delta$ limit with square roots of negative values

Can we strictly prove that smaller delta will still satisfy epsilon in the proof of continuity?

Prove that $f(x)=\begin{cases}0, & x\notin \mathbb{Q}\\ \frac{1}{q}, & x=\frac{p}{q} \text{ in lowest terms}\\ \end{cases}$ is integrable on $[0,1]$.

Proof of the limit of product of sequences

Why we choose $\epsilon_1 <\min \left(1, \frac{\varepsilon}{2 M}\right)$ and $\epsilon_2<\min \left(1, \frac{\varepsilon}{2 (|a|+1)}\right)$

Use the definition of a limit to prove the following: $\lim\limits_{x\to0}\frac{\cos x}{x^{2}}=\infty$

Use the definition of a limit to prove the following: $\lim_{x\to4}\frac{x-2}{\sqrt{x}+2}=\frac{1}{2}$

Necessity of selecting value for $\delta$ in $\epsilon$-$\delta$ proofs

How can I prove that $\lim _{x\to 0}\left(\frac{1}{f\left(x\right)}\right)=\frac{1}{L}$ using the $ε-δ $ argument

Proof writing: $\varepsilon$-$\delta$ proof of the product rule for limits --- any tips for cleaning this up?

When proving $\lim\limits_{x\to2}x^2=4$, can $\delta$ contain $x$?

Prove a limit with $\varepsilon$-$\delta$ definition:

Proof of a quotient when a limit approaches infinity

$ x \sin(\frac{1}{x}) $ Riemann integrable on [-1,1]?

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