Question

Why $\lim_{n\to \infty} \left(1+ \frac 1n \right)^n=e$ doesn't imply $\lim_{n\to \infty} \left(1+\frac 1n \right)≠1?$

score 146 · Answer 1 · 2026-04-10 01:33:54

146

Views

Why $\lim_{n\to \infty} \left(1+ \frac 1n \right)^n=e$ doesn't imply $\lim_{n\to \infty} \left(1+\frac 1n \right)≠1?$

Published on 10 Apr 2026 - 1:33

score 394 · Answer 2 · 2026-04-15 07:55:11

394

Views

Delta Epsilon Proof for Ratio of Polynomials

Published on 15 Apr 2026 - 7:55

score 88 · Answer 3 · 2026-04-16 05:02:37

88

Views

Limit as $x\to\infty$ of $(x+3)^x/f_1(x)$, where $f_1(x)=\sum\limits_{n=3}^{x+2}n^x$

Published on 16 Apr 2026 - 5:02

score 338 · Answer 4 · 2026-04-13 19:43:13

338

Views

Multivariable delta-epsilon limit proofs

Published on 13 Apr 2026 - 19:43

score 499 · Answer 5 · 2026-04-15 18:39:32

499

Views

How to prove that $\lim_{x\to 0}\frac{x}{\sin x}=1$, knowing that $\lim_{x\to 0}\frac{\sin x}{x}=1$?

Published on 15 Apr 2026 - 18:39

score 37 · Answer 6 · 2026-04-16 07:54:37

37

Views

Why does $c$ in mean value theorem converge to $a$ and $b$, where $a < c < b$?

Published on 16 Apr 2026 - 7:54

score 130 · Answer 7 · 2026-04-17 02:33:57

130

Views

Calculate limit of $\lim_{n \to \infty}4\sqrt{n+3}-\sqrt{n-1}-5\sqrt{n+7}+2\sqrt{n-3}$

Published on 17 Apr 2026 - 2:33

score 155 · Answer 8 · 2026-04-16 13:35:53

155

Views

$\lim_{n\rightarrow \infty} n^\alpha (\sqrt[5]{n^2+n}-\sqrt[5]{n^2+2n+1})$

Published on 16 Apr 2026 - 13:35

score 122 · Answer 9 · 2026-04-12 14:59:33

122

Views

How to find $\lim_{x\to\infty} {\sin x \over x}$ without squeeze theorem?

Published on 12 Apr 2026 - 14:59

score 457 · Answer 10 · 2026-04-17 02:46:17

457

Views

Prove that the sequence $b_n = 1$, $b_{n+1} = \frac{1}{1+b_n}$ converges.

Published on 17 Apr 2026 - 2:46

score 89 · Answer 11 · 2026-04-14 18:13:32

89

Views

Prove that $\lim_{n\rightarrow\infty}\frac{exp(r)}{r^n}=\infty$ from the definition

Published on 14 Apr 2026 - 18:13

score 127 · Answer 12 · 2026-04-16 08:16:39

127

Views

Evaluating $\lim\limits_{x\to\infty}{x\int_0^{\pi/4}{\ln(1+\tan^xt)dt}}$

Published on 16 Apr 2026 - 8:16

score 409 · Answer 13 · 2026-04-16 12:29:05

409

Views

Let $f$ be a function with the IVP and for a fix $y$ let $M$ be $\{x\in\mathbb R\mid f(x)=y\}$. If $M$ is non-empty and bounded, then $\sup M\in M$.

Published on 16 Apr 2026 - 12:29

score 107 · Answer 14 · 2026-03-25 22:30:56

107

Views

Evaluate $\lim\limits_{n\rightarrow \infty} \sum\limits_{r=0}^{\infty} \frac{^n\text{C}_{r}}{n^r(r+4)}$

Published on 25 Mar 2026 - 22:30

score 228 · Answer 15 · 2026-04-14 18:37:16

228

Views

A function with $\lim_{x \to \pm \infty} f(f(x))=\pm \infty$

Published on 14 Apr 2026 - 18:37

List Question

Why $\lim_{n\to \infty} \left(1+ \frac 1n \right)^n=e$ doesn't imply $\lim_{n\to \infty} \left(1+\frac 1n \right)≠1?$

Delta Epsilon Proof for Ratio of Polynomials

Limit as $x\to\infty$ of $(x+3)^x/f_1(x)$, where $f_1(x)=\sum\limits_{n=3}^{x+2}n^x$

Multivariable delta-epsilon limit proofs

How to prove that $\lim_{x\to 0}\frac{x}{\sin x}=1$, knowing that $\lim_{x\to 0}\frac{\sin x}{x}=1$?

Why does $c$ in mean value theorem converge to $a$ and $b$, where $a < c < b$?

Calculate limit of $\lim_{n \to \infty}4\sqrt{n+3}-\sqrt{n-1}-5\sqrt{n+7}+2\sqrt{n-3}$

$\lim_{n\rightarrow \infty} n^\alpha (\sqrt[5]{n^2+n}-\sqrt[5]{n^2+2n+1})$

How to find $\lim_{x\to\infty} {\sin x \over x}$ without squeeze theorem?

Prove that the sequence $b_n = 1$, $b_{n+1} = \frac{1}{1+b_n}$ converges.

Prove that $\lim_{n\rightarrow\infty}\frac{exp(r)}{r^n}=\infty$ from the definition

Evaluating $\lim\limits_{x\to\infty}{x\int_0^{\pi/4}{\ln(1+\tan^xt)dt}}$

Let $f$ be a function with the IVP and for a fix $y$ let $M$ be $\{x\in\mathbb R\mid f(x)=y\}$. If $M$ is non-empty and bounded, then $\sup M\in M$.

Evaluate $\lim\limits_{n\rightarrow \infty} \sum\limits_{r=0}^{\infty} \frac{^n\text{C}_{r}}{n^r(r+4)}$

A function with $\lim_{x \to \pm \infty} f(f(x))=\pm \infty$

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