Question

Proving $\lim_{ x\to 0 } \sin \frac{2\pi }{x}$ does not exist

score 296 · Answer 1 · 2026-04-15 05:38:30

296

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Proving $\lim_{ x\to 0 } \sin \frac{2\pi }{x}$ does not exist

Published on 15 Apr 2026 - 5:38

score 133 · Answer 2 · 2026-04-16 06:26:27

133

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Proving that $\lim_{t\to \infty} r(t) = 1$

Published on 16 Apr 2026 - 6:26

score 106 · Answer 3 · 2026-04-16 07:14:09

106

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Evaluate $\lim_{\mu \to \infty} \int_{\frac{\mu}{2}}^\infty \frac{1}{\sqrt{2\pi}}e^{-\frac{(t-\mu)^2}{2}}dt$

Published on 16 Apr 2026 - 7:14

score 170 · Answer 4 · 2026-05-10 14:56:55

170

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Function $f$ s.t. $\lim_{x\to\infty}\frac{f(e^x)}{f(x)}=1$

Published on 10 May 2026 - 14:56

score 313 · Answer 5 · 2026-05-11 08:41:09

313

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Show that $\frac{X_n-nm}{\sqrt{nm}} \xrightarrow{d}N(0,1) , X_n \in Bin(n^2,m/n),m>0$

Published on 11 May 2026 - 8:41

score 2.5k · Answer 6 · 2026-05-11 01:11:28

2.5k

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F distribution with the denominator degrees of freedom infinitely large

Published on 11 May 2026 - 1:11

score 88 · Answer 7 · 2026-05-11 22:22:55

88

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For what functions is $\lim_{n\to \infty}|f^{(n)}(x)|=0$? (Where $f^{(n)}(x)$ is the $n$th derivative of $f$)

Published on 11 May 2026 - 22:22

score 322 · Answer 8 · 2026-05-10 17:17:39

322

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Why does Spivak say "$dx$ (in $\int f(x) dx$) has no meaning in isolation" in his Calculus textbook?

Published on 10 May 2026 - 17:17

score 1.2k · Answer 9 · 2026-04-09 09:02:01

1.2k

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Finding a limit inside a limit

Published on 09 Apr 2026 - 9:02

score 1.5k · Answer 10 · 2026-04-14 14:41:32

1.5k

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Find values of the constants $k$ and $m$, if possible, that will make the function continuous everywhere.

Published on 14 Apr 2026 - 14:41

score 279 · Answer 11 · 2026-04-15 18:51:17

279

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If $\int_0^\infty f(x) dx=0$ , $f(x)$ continuous for $x\in[0,\infty)$, can it be proved that $\lim_{x\to\infty}f(x)=0$?

Published on 15 Apr 2026 - 18:51

score 366 · Answer 12 · 2026-05-10 17:17:54

366

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Proving that the sequence $1, \frac12, \frac{1/2}{3/4}, \cdots$ converges to $\frac{\sqrt 2}2$

Published on 10 May 2026 - 17:17

score 723 · Answer 13 · 2026-04-17 00:00:24

723

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Interesting limit: $I(n)=\lim_{x \to 0} (e^x-1)^{-n} - \left(\frac{x}{1!}+\frac {x^2}{2!}+\dotsb+\frac{x^n}{n!}\right)^{-n}$

Published on 17 Apr 2026 - 0:00

score 413 · Answer 14 · 2026-05-07 12:50:24

413

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Finding limit from Squeeze theorem: $\lim\limits_{n\to\infty} \left(\frac{2n-5}{3n+1}\right)^n$

Published on 07 May 2026 - 12:50

score 1k · Answer 15 · 2026-04-14 08:59:08

1k

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Calculate $\lim_{|\lambda| \to +\infty} \int_{\mathbb{R}}f(x)|\sin(\lambda x)|dx $

Published on 14 Apr 2026 - 8:59

List Question

Proving $\lim_{ x\to 0 } \sin \frac{2\pi }{x}$ does not exist

Proving that $\lim_{t\to \infty} r(t) = 1$

Evaluate $\lim_{\mu \to \infty} \int_{\frac{\mu}{2}}^\infty \frac{1}{\sqrt{2\pi}}e^{-\frac{(t-\mu)^2}{2}}dt$

Function $f$ s.t. $\lim_{x\to\infty}\frac{f(e^x)}{f(x)}=1$

Show that $\frac{X_n-nm}{\sqrt{nm}} \xrightarrow{d}N(0,1) , X_n \in Bin(n^2,m/n),m>0$

F distribution with the denominator degrees of freedom infinitely large

For what functions is $\lim_{n\to \infty}|f^{(n)}(x)|=0$? (Where $f^{(n)}(x)$ is the $n$th derivative of $f$)

Why does Spivak say "$dx$ (in $\int f(x) dx$) has no meaning in isolation" in his Calculus textbook?

Finding a limit inside a limit

Find values of the constants $k$ and $m$, if possible, that will make the function continuous everywhere.

If $\int_0^\infty f(x) dx=0$ , $f(x)$ continuous for $x\in[0,\infty)$, can it be proved that $\lim_{x\to\infty}f(x)=0$?

Proving that the sequence $1, \frac12, \frac{1/2}{3/4}, \cdots$ converges to $\frac{\sqrt 2}2$

Interesting limit: $I(n)=\lim_{x \to 0} (e^x-1)^{-n} - \left(\frac{x}{1!}+\frac {x^2}{2!}+\dotsb+\frac{x^n}{n!}\right)^{-n}$

Finding limit from Squeeze theorem: $\lim\limits_{n\to\infty} \left(\frac{2n-5}{3n+1}\right)^n$

Calculate $\lim_{|\lambda| \to +\infty} \int_{\mathbb{R}}f(x)|\sin(\lambda x)|dx $

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