Question

Evaluate $\lim_{x\rightarrow \infty}\frac{\ln \left( \sqrt[x]{a_1^x+a_2^x+...+a_n^x}-a_1 \right)}{x}$

score 160 · Answer 1 · 2018-04-18 14:16:49

Evaluate $\lim_{x\rightarrow \infty}\frac{\ln \left( \sqrt[x]{a_1^x+a_2^x+...+a_n^x}-a_1 \right)}{x}$

Published on 18 Apr 2018 - 14:16

score 60 · Answer 2 · 2018-04-18 17:06:45

Counterexamples to "If $\lim_{x\to \infty} f(x)=0$, then for large enough $x$,$f(x)$ gets closer and closer to $0$, without ever equalling $0$."

score 69 · Answer 3 · 2018-04-18 23:24:27

69

Views

Limit of the logarithm of values very close to one: $\frac{\ln(1-\epsilon_A^2)}{\ln(1-\epsilon_B^2)}$

Published on 18 Apr 2018 - 23:24

score 50 · Answer 4 · 2018-04-20 16:42:48

50

Views

How to solve this limit

Published on 20 Apr 2018 - 16:42

score 125 · Answer 5 · 2018-04-20 19:51:27

125

Views

Proving $x^{1/x}$ approaches $1$ as $x$ approaches infinity

Published on 20 Apr 2018 - 19:51

score 119 · Answer 6 · 2018-04-21 00:56:47

119

Views

Evaluate without L'Hopital: $\lim_{x\to1}\left\{\frac{9}{x^9-1}-\frac{5}{x^5-1}\right\}$

Published on 21 Apr 2018 - 0:56

score 167 · Answer 7 · 2018-04-21 02:30:30

167

Views

Calculating $\lim\limits_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}$ without L'Hospital

Published on 21 Apr 2018 - 2:30

score 402 · Answer 8 · 2018-04-22 22:21:44

402

Views

How to answer Calculus by Michael Spivak Chapter 5 problem 15.IX

Published on 22 Apr 2018 - 22:21

score 140 · Answer 9 · 2018-04-23 00:21:02

140

Views

Trouble calculating the limit $\lim_{x\to\infty} \frac{e^{-x}}{x^{-1}}$

Published on 23 Apr 2018 - 0:21

score 57 · Answer 10 · 2018-04-23 09:23:37

57

Views

Computing a limit involving exponential functiom

Published on 23 Apr 2018 - 9:23

score 70 · Answer 11 · 2018-04-25 09:09:04

70

Views

Limit of a function in R^2 at a point.

Published on 25 Apr 2018 - 9:09

score 78 · Answer 12 · 2018-04-25 17:12:43

78

Views

How to solve this limit? (2)

Published on 25 Apr 2018 - 17:12

score 94 · Answer 13 · 2026-03-25 04:43:35

94

Views

Find $cot\space x_n$ if $sin(x_{n+1}-x_n)+2^{-(n+1)}sin\space x_nsin \space x_{n+1}=0$ for $n\ge1$

Published on 25 Mar 2026 - 4:43

score 137 · Answer 14 · 2018-04-27 11:05:14

137

Views

Evaluating $\lim _{x\to \infty} (\sqrt[3]{(x+1)(x+2)(x+3)}-x)$

Published on 27 Apr 2018 - 11:05

score 242 · Answer 15 · 2018-04-27 17:33:34

242

Views

Find $\lim_{n\to \infty}\{(1+\frac{1}{2n})\cdot (1+\frac{3}{2n}) \cdot (1+\frac{5}{2n})\cdots(1+\frac{2n-1}{2n})\}^{{1}/{2n}}$

Published on 27 Apr 2018 - 17:33

List Question

Evaluate $\lim_{x\rightarrow \infty}\frac{\ln \left( \sqrt[x]{a_1^x+a_2^x+...+a_n^x}-a_1 \right)}{x}$

Counterexamples to "If $\lim_{x\to \infty} f(x)=0$, then for large enough $x$,$f(x)$ gets closer and closer to $0$, without ever equalling $0$."

Limit of the logarithm of values very close to one: $\frac{\ln(1-\epsilon_A^2)}{\ln(1-\epsilon_B^2)}$

How to solve this limit

Proving $x^{1/x}$ approaches $1$ as $x$ approaches infinity

Evaluate without L'Hopital: $\lim_{x\to1}\left\{\frac{9}{x^9-1}-\frac{5}{x^5-1}\right\}$

Calculating $\lim\limits_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}$ without L'Hospital

How to answer Calculus by Michael Spivak Chapter 5 problem 15.IX

Trouble calculating the limit $\lim_{x\to\infty} \frac{e^{-x}}{x^{-1}}$

Computing a limit involving exponential functiom

Limit of a function in R^2 at a point.

How to solve this limit? (2)

Find $cot\space x_n$ if $sin(x_{n+1}-x_n)+2^{-(n+1)}sin\space x_nsin \space x_{n+1}=0$ for $n\ge1$

Evaluating $\lim _{x\to \infty} (\sqrt[3]{(x+1)(x+2)(x+3)}-x)$

Find $\lim_{n\to \infty}\{(1+\frac{1}{2n})\cdot (1+\frac{3}{2n}) \cdot (1+\frac{5}{2n})\cdots(1+\frac{2n-1}{2n})\}^{{1}/{2n}}$

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