Question

$\epsilon - \delta$ proof of $\lim\limits_{x \rightarrow a} 7x^2$ for all $a \in \mathbb{R}$

score 289 · Answer 1 · 2019-10-19 09:37:49

289

Views

$\epsilon - \delta$ proof of $\lim\limits_{x \rightarrow a} 7x^2$ for all $a \in \mathbb{R}$

Published on 19 Oct 2019 - 9:37

score 243 · Answer 2 · 2019-10-19 22:56:58

243

Views

Understanding the proof of Excercise 10b from chapter 5 of Spivak’s Calculus.

Published on 19 Oct 2019 - 22:56

score 757 · Answer 3 · 2019-10-20 16:36:20

757

Views

Proving $\lim_{x\to 4} \left(\frac{\sqrt {2x-1}}{\sqrt {x-3}}\right) = \sqrt 7$ using $ \varepsilon - \delta$

Published on 20 Oct 2019 - 16:36

score 146 · Answer 4 · 2019-10-20 18:24:06

146

Views

What is the scope of the existential quantifier in the epsilon-delta definition of a limit?

Published on 20 Oct 2019 - 18:24

score 301 · Answer 5 · 2019-10-20 18:57:35

301

Views

Epsilon - delta proof: $\lim\limits_{x\to\frac\pi2} \tan x$ does not exist.

Published on 20 Oct 2019 - 18:57

score 939 · Answer 6 · 2019-10-21 00:13:55

939

Views

Show that if for continuous functions $f,g$, $f(x)=g(x)$ for all $x\in S$, where $S$ is a dense subset of $\mathbb R$, then $f=g$.

Published on 21 Oct 2019 - 0:13

score 113 · Answer 7 · 2019-10-21 19:13:02

113

Views

help solving for delta in epsilon delta proof

Published on 21 Oct 2019 - 19:13

score 375 · Answer 8 · 2019-10-22 18:01:04

375

Views

Is this proof of the limit of the product of a bounded function and a function that goes to zero correct?

Published on 22 Oct 2019 - 18:01

score 28 · Answer 9 · 2019-10-22 23:58:36

28

Views

$\exists δ>0 \forall x \in(x_0-δ,x_0+δ) \cap E^c[|f(x)-f(x_0)|<ε]$

Published on 22 Oct 2019 - 23:58

score 116 · Answer 10 · 2026-02-23 06:41:06

116

Views

Existence of finite and $\sigma$-finite measures, such that $\nu << \mu$ and $\varepsilon$-$\delta$-criterion holds

Published on 23 Feb 2026 - 6:41

score 43 · Answer 11 · 2019-10-23 07:24:49

43

Views

Prove with the help of the $\varepsilon$-$n_0$ definition, that $\frac 1 4$ is the limit of the sequence $a_n=\frac{n^2-1}{4n^2+1}$

Published on 23 Oct 2019 - 7:24

score 116 · Answer 12 · 2019-10-23 18:23:46

116

Views

Prove that $\lim_{x\to0, y\to0}\frac{x^3+y^3}{x^2+y^2}=0$

Published on 23 Oct 2019 - 18:23

score 86 · Answer 13 · 2019-10-23 18:46:34

86

Views

Prove $\lim_{x\to a} f(x)$ exists $\implies \lim_{x\to a} f(x^2)$ exists

Published on 23 Oct 2019 - 18:46

score 119 · Answer 14 · 2019-10-25 06:58:55

119

Views

Show that $\lim_{(x,y)\to (0,0)}\frac{x^4y^3}{x^2+y^4} = 0$.

Published on 25 Oct 2019 - 6:58

score 279 · Answer 15 · 2019-10-25 14:47:26

279

Views

Using the definition of limit show that $\lim_{x→x_0} x^3=x_0^3$

Published on 25 Oct 2019 - 14:47

List Question

$\epsilon - \delta$ proof of $\lim\limits_{x \rightarrow a} 7x^2$ for all $a \in \mathbb{R}$

Understanding the proof of Excercise 10b from chapter 5 of Spivak’s Calculus.

Proving $\lim_{x\to 4} \left(\frac{\sqrt {2x-1}}{\sqrt {x-3}}\right) = \sqrt 7$ using $ \varepsilon - \delta$

What is the scope of the existential quantifier in the epsilon-delta definition of a limit?

Epsilon - delta proof: $\lim\limits_{x\to\frac\pi2} \tan x$ does not exist.

Show that if for continuous functions $f,g$, $f(x)=g(x)$ for all $x\in S$, where $S$ is a dense subset of $\mathbb R$, then $f=g$.

help solving for delta in epsilon delta proof

Is this proof of the limit of the product of a bounded function and a function that goes to zero correct?

$\exists δ>0 \forall x \in(x_0-δ,x_0+δ) \cap E^c[|f(x)-f(x_0)|<ε]$

Existence of finite and $\sigma$-finite measures, such that $\nu << \mu$ and $\varepsilon$-$\delta$-criterion holds

Prove with the help of the $\varepsilon$-$n_0$ definition, that $\frac 1 4$ is the limit of the sequence $a_n=\frac{n^2-1}{4n^2+1}$

Prove that $\lim_{x\to0, y\to0}\frac{x^3+y^3}{x^2+y^2}=0$

Prove $\lim_{x\to a} f(x)$ exists $\implies \lim_{x\to a} f(x^2)$ exists

Show that $\lim_{(x,y)\to (0,0)}\frac{x^4y^3}{x^2+y^4} = 0$.

Using the definition of limit show that $\lim_{x→x_0} x^3=x_0^3$

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