Question

$ \lim_{x \to \infty} [\frac{x^2+1}{x+1}-ax-b]=0 \ $ then show that $ \ a=1, \ b=-1 \ $

score 569 · Answer 1 · 2026-04-16 12:34:46

569

Views

$ \lim_{x \to \infty} [\frac{x^2+1}{x+1}-ax-b]=0 \ $ then show that $ \ a=1, \ b=-1 \ $

Published on 16 Apr 2026 - 12:34

score 54 · Answer 2 · 2026-04-11 21:43:21

54

Views

Why sum of zeta's approaches an integer?

Published on 11 Apr 2026 - 21:43

score 161 · Answer 3 · 2026-04-16 13:59:23

161

Views

Find a $\delta$ such that $\lvert \sqrt{x} - 1 \rvert<\varepsilon$ for all $x$ satisfying $0<\lvert x-1 \rvert <\delta$

Published on 16 Apr 2026 - 13:59

score 146 · Answer 4 · 2026-04-11 17:09:13

146

Views

How can I find an $\varepsilon$ environment to disprove $\lim_{n\to \infty}(\{{\sqrt{n}}\}) = 0$?

Published on 11 Apr 2026 - 17:09

score 116 · Answer 5 · 2026-04-11 06:45:03

116

Views

The limit as x approaches to infinity where c is a constant

Published on 11 Apr 2026 - 6:45

score 325 · Answer 6 · 2026-04-21 13:07:08

325

Views

Limit: $\lim_{x\to 0}\frac{x^3 - 3x^2+1}{x^3}$

Published on 21 Apr 2026 - 13:07

score 132 · Answer 7 · 2026-04-15 09:32:45

132

Views

prove that $\lim_{x\to 0^{-}}\frac{x}{|x|}$

Published on 15 Apr 2026 - 9:32

score 56 · Answer 8 · 2026-04-16 05:02:13

56

Views

$\lim_{x \rightarrow 0^+} e^{-1/x}/x^3$

Published on 16 Apr 2026 - 5:02

score 28 · Answer 9 · 2026-04-15 10:55:21

28

Views

if $\boldsymbol{f(x)}$ is not convergent, can $\boldsymbol{f(x)}$ be separated in limit?

Published on 15 Apr 2026 - 10:55

score 91 · Answer 10 · 2026-04-16 09:26:16

91

Views

Determine the limit of $\frac1n \sum\limits_{i=1}^n i^\frac{1}{i}$ as ${n \to \infty}$ .

Published on 16 Apr 2026 - 9:26

score 166 · Answer 11 · 2026-04-14 17:42:31

166

Views

$\lim_{n\to\infty} 1^n = 1$?

Published on 14 Apr 2026 - 17:42

score 148 · Answer 12 · 2026-04-08 16:22:19

148

Views

Proof explanation: Convergence of a series

Published on 08 Apr 2026 - 16:22

score 126 · Answer 13 · 2026-04-16 06:47:24

126

Views

How to find the limit $lim_{t \to0+}\frac{e^{-1/t}}{\sqrt t}$

Published on 16 Apr 2026 - 6:47

score 67 · Answer 14 · 2026-04-16 15:01:53

67

Views

How can I calculate the limit $\lim_{x \to \infty} \left(\frac{f(x)+g(x)}{f(x)^4 + g(x)^4}\right)$?

Published on 16 Apr 2026 - 15:01

score 1.6k · Answer 15 · 2026-04-10 08:56:27

1.6k

Views

Show convergence by using partial fractions

Published on 10 Apr 2026 - 8:56

List Question

$ \lim_{x \to \infty} [\frac{x^2+1}{x+1}-ax-b]=0 \ $ then show that $ \ a=1, \ b=-1 \ $

Why sum of zeta's approaches an integer?

Find a $\delta$ such that $\lvert \sqrt{x} - 1 \rvert<\varepsilon$ for all $x$ satisfying $0<\lvert x-1 \rvert <\delta$

How can I find an $\varepsilon$ environment to disprove $\lim_{n\to \infty}(\{{\sqrt{n}}\}) = 0$?

The limit as x approaches to infinity where c is a constant

Limit: $\lim_{x\to 0}\frac{x^3 - 3x^2+1}{x^3}$

prove that $\lim_{x\to 0^{-}}\frac{x}{|x|}$

$\lim_{x \rightarrow 0^+} e^{-1/x}/x^3$

if $\boldsymbol{f(x)}$ is not convergent, can $\boldsymbol{f(x)}$ be separated in limit?

Determine the limit of $\frac1n \sum\limits_{i=1}^n i^\frac{1}{i}$ as ${n \to \infty}$ .

$\lim_{n\to\infty} 1^n = 1$?

Proof explanation: Convergence of a series

How to find the limit $lim_{t \to0+}\frac{e^{-1/t}}{\sqrt t}$

How can I calculate the limit $\lim_{x \to \infty} \left(\frac{f(x)+g(x)}{f(x)^4 + g(x)^4}\right)$?

Show convergence by using partial fractions

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