Question

If $c > 1$, show that $\sqrt[n]{c}$ approaches $1$ for large $n$.

score 145 · Answer 1 · 2022-12-07 04:49:55

145

Views

If $c > 1$, show that $\sqrt[n]{c}$ approaches $1$ for large $n$.

Published on 07 Dec 2022 - 4:49

score 132 · Answer 2 · 2022-12-07 20:32:05

132

Views

Epsilon-delta proof the limit of a logarithm

Published on 07 Dec 2022 - 20:32

score 632 · Answer 3 · 2026-02-26 15:42:47

632

Views

If $(f_n)$ converges pointwise to $f$, then $f$ is uniformly continuous

Published on 26 Feb 2026 - 15:42

score 52 · Answer 4 · 2022-12-14 15:16:12

52

Views

if $f(x)=g(x)$ when $|x-a|<\lambda$.prove that $\lim_{x \to a} f(x)=\lim_{x \to a} g(x)$

Published on 14 Dec 2022 - 15:16

score 66 · Answer 5 · 2022-12-14 21:48:01

66

Views

if $f(x)=g(x)$ when $|x-a|<\lambda$,prove that $\lim_{x \to a} f(x)=\lim_{x \to a} g(x)$

Published on 14 Dec 2022 - 21:48

score 31 · Answer 6 · 2022-12-15 19:57:47

31

Views

if $\lim_{x\to 0 } f(x)=l$ ,then there is a number $\lambda >0$ and a number $M$ such that $|f(x)|<M$ if $|x-a|<\lambda$

Published on 15 Dec 2022 - 19:57

score 113 · Answer 7 · 2022-12-20 22:20:33

113

Views

how to prove that the following limit doesn't exist when puting L=3 using epsilon-delta definition?

Published on 20 Dec 2022 - 22:20

score 88 · Answer 8 · 2022-12-21 11:44:53

88

Views

Given $\epsilon > 0$, show that the unit disc contains finitely many dyadic squares whose total area exceeds $\pi - \epsilon$

Published on 21 Dec 2022 - 11:44

score 84 · Answer 9 · 2022-12-22 02:51:07

84

Views

A simple question related to the Stolz–Cesàro theorem

Published on 22 Dec 2022 - 2:51

score 102 · Answer 10 · 2022-12-22 19:34:57

102

Views

Proving $\lim_{x \to c}f(g(x)) = f( \lim_{x \to c} g(x))=f(L) \text{ where } \lim_{x \to c} g(x) = L \text{ and } f(x) \text{ is continuous at } x=L$

Published on 22 Dec 2022 - 19:34

score 50 · Answer 11 · 2022-12-23 11:30:32

50

Views

Problem understanding $\epsilon-\delta$ definition of continuity - a particular example.

Published on 23 Dec 2022 - 11:30

score 196 · Answer 12 · 2026-04-08 04:14:17

196

Views

Showing that $u_n=\sum_{k=0}^{n}\frac{1}{k!}$ is Cauchy

Published on 08 Apr 2026 - 4:14

score 71 · Answer 13 · 2026-04-06 12:57:11

71

Views

An exercise I made for myself on Uniform Continuity and couldn't solve

Published on 06 Apr 2026 - 12:57

score 107 · Answer 14 · 2026-03-27 07:14:18

107

Views

Proving discontinuity at $\,x =1\,$ using $\,\varepsilon$-$\delta\,$ definition

Published on 27 Mar 2026 - 7:14

score 64 · Answer 15 · 2026-04-09 05:26:31

64

Views

Determining delta graphically from limit definition

Published on 09 Apr 2026 - 5:26

List Question

If $c > 1$, show that $\sqrt[n]{c}$ approaches $1$ for large $n$.

Epsilon-delta proof the limit of a logarithm

If $(f_n)$ converges pointwise to $f$, then $f$ is uniformly continuous

if $f(x)=g(x)$ when $|x-a|<\lambda$.prove that $\lim_{x \to a} f(x)=\lim_{x \to a} g(x)$

if $f(x)=g(x)$ when $|x-a|<\lambda$,prove that $\lim_{x \to a} f(x)=\lim_{x \to a} g(x)$

if $\lim_{x\to 0 } f(x)=l$ ,then there is a number $\lambda >0$ and a number $M$ such that $|f(x)|<M$ if $|x-a|<\lambda$

how to prove that the following limit doesn't exist when puting L=3 using epsilon-delta definition?

Given $\epsilon > 0$, show that the unit disc contains finitely many dyadic squares whose total area exceeds $\pi - \epsilon$

A simple question related to the Stolz–Cesàro theorem

Proving $\lim_{x \to c}f(g(x)) = f( \lim_{x \to c} g(x))=f(L) \text{ where } \lim_{x \to c} g(x) = L \text{ and } f(x) \text{ is continuous at } x=L$

Problem understanding $\epsilon-\delta$ definition of continuity - a particular example.

Showing that $u_n=\sum_{k=0}^{n}\frac{1}{k!}$ is Cauchy

An exercise I made for myself on Uniform Continuity and couldn't solve

Proving discontinuity at $\,x =1\,$ using $\,\varepsilon$-$\delta\,$ definition

Determining delta graphically from limit definition

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