Question

Evaluate $\lim_{x\rightarrow0}\frac{e^x-e^{-x}}{e^x-1}$

score 117 · Answer 1 · 2026-04-17 07:47:06

117

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Evaluate $\lim_{x\rightarrow0}\frac{e^x-e^{-x}}{e^x-1}$

Published on 17 Apr 2026 - 7:47

score 81 · Answer 2 · 2026-04-16 10:51:19

81

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Find the limit of $x(x + 1 - \sin(\frac{1}{1+x})^{-1})$ as $x \rightarrow \infty$

Published on 16 Apr 2026 - 10:51

score 141 · Answer 3 · 2026-04-16 07:38:17

141

Views

$\underset{x \to 0}{\lim}(1 + g(x))^\frac{1}{f(x)} = e^{\underset{x \to 0}{\lim}\frac {g(x)}{f(x)}}$.

Published on 16 Apr 2026 - 7:38

score 58 · Answer 4 · 2026-04-14 06:24:47

58

Views

Am I choosing the correct sequences to show this limit does not exist?

Published on 14 Apr 2026 - 6:24

score 78 · Answer 5 · 2026-04-10 00:40:45

78

Views

What is meant with $\lim_{h \to 0} f(x+h)$?

Published on 10 Apr 2026 - 0:40

score 760 · Answer 6 · 2026-04-16 03:19:30

760

Views

Every point of the unit circle is a limit point of $x_k = \left(1+\frac{1}{2^k}\right)\begin{bmatrix} \cos k\\\sin k\\ \end{bmatrix}$

Published on 16 Apr 2026 - 3:19

score 60 · Answer 7 · 2026-04-14 18:46:39

60

Views

If a sum of $L$ positive integers grows like $L^d$, how does the summand grow?

Published on 14 Apr 2026 - 18:46

score 46 · Answer 8 · 2026-04-15 07:05:19

46

Views

Unnecessary use of left and right limits?

Published on 15 Apr 2026 - 7:05

score 147 · Answer 9 · 2026-04-14 10:21:55

147

Views

How do you solve $\lim_{n\to \infty}{n[(1+\frac{c}{n})^{n}-(1-\frac{c}{n})^{-n}]}$ without L’Hopital's Rule?

Published on 14 Apr 2026 - 10:21

score 324 · Answer 10 · 2026-05-04 10:00:15

324

Views

Can nested limits be flattened into a single limit?

Published on 04 May 2026 - 10:00

score 970 · Answer 11 · 2026-04-11 20:39:47

970

Views

Why this limit exists (Khan Academy)

Published on 11 Apr 2026 - 20:39

score 1.8k · Answer 12 · 2026-04-17 13:47:39

1.8k

Views

Evaluate $\lim_{x \to \infty} [(x+2)\tan^{-1}(x+2) -x \tan^{-1}x]$

Published on 17 Apr 2026 - 13:47

score 1.8k · Answer 13 · 2026-04-09 06:31:24

1.8k

Views

Limits of combined functions Problem (Khan Academy)

Published on 09 Apr 2026 - 6:31

score 130 · Answer 14 · 2026-04-15 12:41:18

130

Views

Proving convergence of sequence using epsilon-N

Published on 15 Apr 2026 - 12:41

score 450 · Answer 15 · 2026-05-10 22:02:34

450

Views

Given that $\lim\limits_{n \to \infty}\left(1+\frac{1}{n}\right)^n=e$, show that $1+\frac{1}{1!}+\frac{1}{2!}+\cdots=e$.

Published on 10 May 2026 - 22:02

List Question

Evaluate $\lim_{x\rightarrow0}\frac{e^x-e^{-x}}{e^x-1}$

Find the limit of $x(x + 1 - \sin(\frac{1}{1+x})^{-1})$ as $x \rightarrow \infty$

$\underset{x \to 0}{\lim}(1 + g(x))^\frac{1}{f(x)} = e^{\underset{x \to 0}{\lim}\frac {g(x)}{f(x)}}$.

Am I choosing the correct sequences to show this limit does not exist?

What is meant with $\lim_{h \to 0} f(x+h)$?

Every point of the unit circle is a limit point of $x_k = \left(1+\frac{1}{2^k}\right)\begin{bmatrix} \cos k\\\sin k\\ \end{bmatrix}$

If a sum of $L$ positive integers grows like $L^d$, how does the summand grow?

Unnecessary use of left and right limits?

How do you solve $\lim_{n\to \infty}{n[(1+\frac{c}{n})^{n}-(1-\frac{c}{n})^{-n}]}$ without L’Hopital's Rule?

Can nested limits be flattened into a single limit?

Why this limit exists (Khan Academy)

Evaluate $\lim_{x \to \infty} [(x+2)\tan^{-1}(x+2) -x \tan^{-1}x]$

Limits of combined functions Problem (Khan Academy)

Proving convergence of sequence using epsilon-N

Given that $\lim\limits_{n \to \infty}\left(1+\frac{1}{n}\right)^n=e$, show that $1+\frac{1}{1!}+\frac{1}{2!}+\cdots=e$.

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