Question

Finding $\lim_{(x,y)\to (1,0)} \frac{(x-1)^2\log(x)}{(x-1)^2 + y^2}$ if it exists

score 151 · Answer 1 · 2022-02-09 14:07:31

151

Views

Finding $\lim_{(x,y)\to (1,0)} \frac{(x-1)^2\log(x)}{(x-1)^2 + y^2}$ if it exists

Published on 09 Feb 2022 - 14:07

score 65 · Answer 2 · 2022-02-09 23:40:53

65

Views

What is the reason that epsilon delta definition says the result of multiplying upper bound and $|x-a|$ is less than $\epsilon$?

Published on 09 Feb 2022 - 23:40

score 1.9k · Answer 3 · 2022-02-12 21:31:27

1.9k

Views

If $f:\mathbb{R}\to\mathbb{R}$ is continuous at $x=0$ and $f(x+y)=f(x)+f(y)$, then $f$ is continuous at every point in $\mathbb{R}$.

Published on 12 Feb 2022 - 21:31

score 675 · Answer 4 · 2022-02-14 15:08:46

675

Views

Is it crucial for an engineering student to "master" the epsilon-delta definitions of limits?

Published on 14 Feb 2022 - 15:08

score 57 · Answer 5 · 2022-02-17 09:24:17

57

Views

In epsilon n proofs, how is the index of the sequence related to the expression n>N

Published on 17 Feb 2022 - 9:24

score 94 · Answer 6 · 2022-02-19 16:51:55

94

Views

I don't understand what I'm doing wrong: Prove that $f(x) = x^3$ is continuous at $x = −2$.

Published on 19 Feb 2022 - 16:51

score 107 · Answer 7 · 2026-04-07 14:41:59

107

Views

Proving Riemann Integrability if only if there exists $L \in \mathbb{R}$ (Bartle's exercise 7.1 no.3)

Published on 07 Apr 2026 - 14:41

score 394 · Answer 8 · 2022-02-22 13:21:45

394

Views

Prove that $\lim_{x \to 0} x \sin\left(\frac1x\right)=0$

Published on 22 Feb 2022 - 13:21

score 67 · Answer 9 · 2026-04-08 04:46:09

67

Views

Proof using Epsilon Delta definition of proof. [Read Description]

Published on 08 Apr 2026 - 4:46

score 98 · Answer 10 · 2022-02-26 18:01:47

98

Views

Prove that $\lim\limits_{z\to0}z+\vert{z}\vert^3=0$. Epsilon-Delta proof.

Published on 26 Feb 2022 - 18:01

score 89 · Answer 11 · 2026-02-26 07:58:21

89

Views

Uniform convergence and rigor proof of pointwise convergence of $f_n(x)=n\left(\sqrt{x+\frac1n}- \sqrt{x}\right)$ for all $x \in (0,\infty)$.

Published on 26 Feb 2026 - 7:58

score 128 · Answer 12 · 2022-03-04 13:43:20

128

Views

How can you prove that $\lim_{x \to \infty} \frac{x^{100}}{1.01^x} = 0$ using definition of limit?

Published on 04 Mar 2022 - 13:43

score 115 · Answer 13 · 2026-04-07 16:10:30

115

Views

Rational Epsilon-Delta Limit Proof Questions

Published on 07 Apr 2026 - 16:10

score 153 · Answer 14 · 2022-03-07 14:19:06

153

Views

Epsilon delta proof of nested sine function

Published on 07 Mar 2022 - 14:19

score 185 · Answer 15 · 2022-03-09 18:46:36

185

Views

Let $g$ be continuous on an interval $A$ and let $F$ be the set of points where $g$ fails to be one-to-one. Show $F$ is either empty or uncountable.

Published on 09 Mar 2022 - 18:46

List Question

Finding $\lim_{(x,y)\to (1,0)} \frac{(x-1)^2\log(x)}{(x-1)^2 + y^2}$ if it exists

What is the reason that epsilon delta definition says the result of multiplying upper bound and $|x-a|$ is less than $\epsilon$?

If $f:\mathbb{R}\to\mathbb{R}$ is continuous at $x=0$ and $f(x+y)=f(x)+f(y)$, then $f$ is continuous at every point in $\mathbb{R}$.

Is it crucial for an engineering student to "master" the epsilon-delta definitions of limits?

In epsilon n proofs, how is the index of the sequence related to the expression n>N

I don't understand what I'm doing wrong: Prove that $f(x) = x^3$ is continuous at $x = −2$.

Proving Riemann Integrability if only if there exists $L \in \mathbb{R}$ (Bartle's exercise 7.1 no.3)

Prove that $\lim_{x \to 0} x \sin\left(\frac1x\right)=0$

Proof using Epsilon Delta definition of proof. [Read Description]

Prove that $\lim\limits_{z\to0}z+\vert{z}\vert^3=0$. Epsilon-Delta proof.

Uniform convergence and rigor proof of pointwise convergence of $f_n(x)=n\left(\sqrt{x+\frac1n}- \sqrt{x}\right)$ for all $x \in (0,\infty)$.

How can you prove that $\lim_{x \to \infty} \frac{x^{100}}{1.01^x} = 0$ using definition of limit?

Rational Epsilon-Delta Limit Proof Questions

Epsilon delta proof of nested sine function

Let $g$ be continuous on an interval $A$ and let $F$ be the set of points where $g$ fails to be one-to-one. Show $F$ is either empty or uncountable.

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