Question

If $\{a_n\}$ is a sequence such that $0\leq a_{m+n}\leq a_m+a_n$, show that $\lim_{n\to\infty}\frac{a_n}{n}$ exists

score 544 · Answer 1 · 2026-05-13 17:46:13

544

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If $\{a_n\}$ is a sequence such that $0\leq a_{m+n}\leq a_m+a_n$, show that $\lim_{n\to\infty}\frac{a_n}{n}$ exists

Published on 13 May 2026 - 17:46

score 109 · Answer 2 · 2026-04-29 01:01:42

109

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How to prove that $\lim_{(x,y) \to (0,0)} \frac{\sqrt{1+x^2+y^2}-1}{\arcsin{\left(x^2+y^2+x \right) }-\arcsin{x}} =0$?

Published on 29 Apr 2026 - 1:01

score 1k · Answer 3 · 2026-04-10 05:33:42

1k

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How to calculate limits of functions rigorously

Published on 10 Apr 2026 - 5:33

score 65 · Answer 4 · 2026-05-13 17:46:14

65

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Calculate $\lim_{n\to\infty} \frac{\sum_{i=1}^n ia_i}{n^2+n}$ given that $a_n \to a$

Published on 13 May 2026 - 17:46

score 87 · Answer 5 · 2026-04-25 19:40:44

87

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Is it true that if continuous $f(x)$ has a limit then $f(nx_0)$ has a limit for any $x_0$?

Published on 25 Apr 2026 - 19:40

score 71 · Answer 6 · 2026-05-11 03:17:21

71

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Is a function $f$ monotone decreasing if $\lim _{x\to b }f\left(x\right)\:=\:0$ and $f\left(x\right) \ge 0$ $\forall x \in [a,b]$?

Published on 11 May 2026 - 3:17

score 386 · Answer 7 · 2026-04-12 09:21:38

386

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Limit with Epsilon - Delta method

Published on 12 Apr 2026 - 9:21

score 54 · Answer 8 · 2026-04-29 13:07:05

54

Views

Exercise 9 Sec. 13.3 Fitzpatrick's Calculus

Published on 29 Apr 2026 - 13:07

score 6.1k · Answer 9 · 2026-05-10 15:43:20

6.1k

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Limit of composite functions

Published on 10 May 2026 - 15:43

score 171 · Answer 10 · 2026-04-14 04:40:35

171

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is $\arcsin(3x-4x^3)$ Non Differentiable at $x=\pm1$

Published on 14 Apr 2026 - 4:40

score 1.8k · Answer 11 · 2026-04-16 06:48:11

1.8k

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Number of points of discontinuity of $[5x]+\{3x\}$

Published on 16 Apr 2026 - 6:48

score 253 · Answer 12 · 2026-04-10 20:07:48

253

Views

Prove $\sin(xy)/x = a$ when $(x,y) \to (0,a)$, using the epsilon-delta definition.

Published on 10 Apr 2026 - 20:07

score 102 · Answer 13 · 2026-04-25 23:34:51

102

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Limit of $e^{-x^n}$

Published on 25 Apr 2026 - 23:34

score 2.1k · Answer 14 · 2026-05-05 06:54:21

2.1k

Views

Limit of y(x) in Second Order Differential Equation

Published on 05 May 2026 - 6:54

score 93 · Answer 15 · 2026-04-11 15:24:10

93

Views

A Confusing Limit

Published on 11 Apr 2026 - 15:24

List Question

If $\{a_n\}$ is a sequence such that $0\leq a_{m+n}\leq a_m+a_n$, show that $\lim_{n\to\infty}\frac{a_n}{n}$ exists

How to prove that $\lim_{(x,y) \to (0,0)} \frac{\sqrt{1+x^2+y^2}-1}{\arcsin{\left(x^2+y^2+x \right) }-\arcsin{x}} =0$?

How to calculate limits of functions rigorously

Calculate $\lim_{n\to\infty} \frac{\sum_{i=1}^n ia_i}{n^2+n}$ given that $a_n \to a$

Is it true that if continuous $f(x)$ has a limit then $f(nx_0)$ has a limit for any $x_0$?

Is a function $f$ monotone decreasing if $\lim _{x\to b }f\left(x\right)\:=\:0$ and $f\left(x\right) \ge 0$ $\forall x \in [a,b]$?

Limit with Epsilon - Delta method

Exercise 9 Sec. 13.3 Fitzpatrick's Calculus

Limit of composite functions

is $\arcsin(3x-4x^3)$ Non Differentiable at $x=\pm1$

Number of points of discontinuity of $[5x]+\{3x\}$

Prove $\sin(xy)/x = a$ when $(x,y) \to (0,a)$, using the epsilon-delta definition.

Limit of $e^{-x^n}$

Limit of y(x) in Second Order Differential Equation

A Confusing Limit

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