Question

Limit of the integrals of a sequence of function.

score 22 · Answer 1 · 2026-04-14 15:43:58

Limit of the integrals of a sequence of function.

Published on 14 Apr 2026 - 15:43

score 277 · Answer 2 · 2026-05-14 20:12:02

Prove or disprove each of the follow function has limits $x \to a$ by the definition $\lim_{(x, y) \to (0, 0)} \frac{xy^2}{x^2 + y^2}$

score 57 · Answer 3 · 2026-05-10 23:31:41

57

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If $\lim_{n \rightarrow \infty }s_n = s$, is it true that $\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{k=1}^n s_k =s $ as well?

Published on 10 May 2026 - 23:31

score 235 · Answer 4 · 2026-04-09 23:38:40

235

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Behaviour of little-o in equivalence

Published on 09 Apr 2026 - 23:38

score 98 · Answer 5 · 2026-04-16 02:31:17

98

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If $\lim_{x\to0} f(x) = L$ then $\lim_{x\to \infty }f(1/x) = L$ . Is the converse true?

Published on 16 Apr 2026 - 2:31

score 119 · Answer 6 · 2026-04-16 02:47:40

119

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Is $\lim_{n \to \infty} \left(1+\dfrac {x}{n} \right)^{n-1} = e^x$

Published on 16 Apr 2026 - 2:47

score 683 · Answer 7 · 2026-04-16 14:17:47

683

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If {$|a_n|$} is divergent, can {$a_n$} be convergent? If {$a_n^2$} is convergent, can {$a_n$} be divergent?

Published on 16 Apr 2026 - 14:17

score 70 · Answer 8 · 2026-04-16 03:02:03

70

Views

$\lim \frac{x}{\sin x} = +\infty$ or $-\infty $ as $ x \rightarrow (n\pi) , n \neq 0$ is a wrong statement.

Published on 16 Apr 2026 - 3:02

score 222 · Answer 9 · 2026-04-17 00:34:45

222

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Evalutation of the limit $\;\lim\limits_{x \to+ \infty}\left[x - x^2 \cdot \ln\left(1+ \frac 1 x\right)\right]$

Published on 17 Apr 2026 - 0:34

score 102 · Answer 10 · 2026-04-15 10:22:11

102

Views

Prove that $\lim_{x \to 0} f(x) = L\ \Rightarrow \lim_{x \to 0} \left[ 3f(2x) \right] = 3L$.

Published on 15 Apr 2026 - 10:22

score 3k · Answer 11 · 2026-04-11 13:38:09

3k

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Limit when $z$ goes to $0$ of $re(z) / im(z)$?

Published on 11 Apr 2026 - 13:38

score 2.1k · Answer 12 · 2026-05-15 22:45:40

2.1k

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Prove the limit superior of a bounded sequence converges

Published on 15 May 2026 - 22:45

score 201 · Answer 13 · 2026-04-15 23:00:29

201

Views

Show $(a_n)_{n=1}^\infty$ converges to $L \in \mathbb{R}$ iff the limit superior and limit inferior converge to $L$

Published on 15 Apr 2026 - 23:00

score 91 · Answer 14 · 2026-04-11 08:48:28

91

Views

Limit distribution equal to Dirac delta

Published on 11 Apr 2026 - 8:48

score 21 · Answer 15 · 2026-05-16 16:07:31

21

Views

Help with the following limit

Published on 16 May 2026 - 16:07

List Question

Limit of the integrals of a sequence of function.

Prove or disprove each of the follow function has limits $x \to a$ by the definition $\lim_{(x, y) \to (0, 0)} \frac{xy^2}{x^2 + y^2}$

If $\lim_{n \rightarrow \infty }s_n = s$, is it true that $\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{k=1}^n s_k =s $ as well?

Behaviour of little-o in equivalence

If $\lim_{x\to0} f(x) = L$ then $\lim_{x\to \infty }f(1/x) = L$ . Is the converse true?

Is $\lim_{n \to \infty} \left(1+\dfrac {x}{n} \right)^{n-1} = e^x$

If {$|a_n|$} is divergent, can {$a_n$} be convergent? If {$a_n^2$} is convergent, can {$a_n$} be divergent?

$\lim \frac{x}{\sin x} = +\infty$ or $-\infty $ as $ x \rightarrow (n\pi) , n \neq 0$ is a wrong statement.

Evalutation of the limit $\;\lim\limits_{x \to+ \infty}\left[x - x^2 \cdot \ln\left(1+ \frac 1 x\right)\right]$

Prove that $\lim_{x \to 0} f(x) = L\ \Rightarrow \lim_{x \to 0} \left[ 3f(2x) \right] = 3L$.

Limit when $z$ goes to $0$ of $re(z) / im(z)$?

Prove the limit superior of a bounded sequence converges

Show $(a_n)_{n=1}^\infty$ converges to $L \in \mathbb{R}$ iff the limit superior and limit inferior converge to $L$

Limit distribution equal to Dirac delta

Help with the following limit

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