Question

The value of $\lim_{h\to 0}\frac{\sin(a+3h)-3\sin(a+2h)+3\sin(a+h)-\sin a}{h^3}$ is?

score 121 · Answer 1 · 2024-01-06 18:36:55

121

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The value of $\lim_{h\to 0}\frac{\sin(a+3h)-3\sin(a+2h)+3\sin(a+h)-\sin a}{h^3}$ is?

Published on 06 Jan 2024 - 18:36

score 22 · Answer 2 · 2024-01-14 12:16:30

22

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Limit of a function with an integral to have a variable in the upper bound

Published on 14 Jan 2024 - 12:16

score 135 · Answer 3 · 2024-01-17 03:30:29

135

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Please identify my mistake: $\lim_{h\to0}\frac{\ln (1+2 h)-2 \ln (1+h)}{h^2}$

Published on 17 Jan 2024 - 3:30

score 172 · Answer 4 · 2024-01-18 08:12:39

172

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Does $\lim_{x \to 1}\left(\frac{x}{[x]}\right)$ exist?

Published on 18 Jan 2024 - 8:12

score 211 · Answer 5 · 2024-01-18 19:45:39

211

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Find $\lim\limits_{x \to 0} \frac{ \sqrt{1+x} - 1} { \sqrt[3]{1+x} - 1}$.

Published on 18 Jan 2024 - 19:45

score 74 · Answer 6 · 2024-01-20 10:33:27

74

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Calculating limit of a function without using L'Hospital

Published on 20 Jan 2024 - 10:33

score 104 · Answer 7 · 2024-01-21 19:25:52

104

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Evaluating $\lim_{x\to 1}\frac{8^x-8}{x-1}$ without using L'Hopital rule

Published on 21 Jan 2024 - 19:25

score 28 · Answer 8 · 2024-01-31 08:51:15

28

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This limit is puzzling me

Published on 31 Jan 2024 - 8:51

score 42 · Answer 9 · 2024-01-31 18:01:42

42

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Nonanalytic function with Taylor series of all orders

Published on 31 Jan 2024 - 18:01

score 179 · Answer 10 · 2026-04-01 17:32:41

179

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If $\lim\limits_{x\to0}f(x)=0$ and $\lim\limits_{x \to 0}\frac{f(2x)-f(x)}{x}=0$ how to rigorously prove that $\lim\limits_{x \to 0}\frac{f(x)}{x}=0$?

Published on 01 Apr 2026 - 17:32

score 348 · Answer 11 · 2024-02-03 06:49:13

348

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With $x_1=1$ and $x_{n+1} = \frac{1}{x_1^2+x_2^2+\dots+x_{n}^2}$show$\lim\limits_{n\to\infty}\frac{x_1+x_2+\dots+x_n}{n^{2/3}}=\frac{\sqrt[3]{9}}{2}$

Published on 03 Feb 2024 - 6:49

score 370 · Answer 12 · 2024-02-03 14:05:05

370

Views

How to solve this limit without using L'Hopital

Published on 03 Feb 2024 - 14:05

score 74 · Answer 13 · 2024-02-09 12:49:05

74

Views

$\lim_{x \rightarrow 0} \frac{(x^2 - x^3) ((x + 1)^\sqrt{2} - 1)}{\log(1 + 4 x) (1 - \cos(2 x))}$

Published on 09 Feb 2024 - 12:49

score 123 · Answer 14 · 2024-02-10 02:07:59

123

Views

A limit of $1^\infty$ form (maybe)

Published on 10 Feb 2024 - 2:07

score 90 · Answer 15 · 2024-02-10 09:48:34

90

Views

Without using L'Hopitals rule, how do you get $\lim_{x \to 0} \frac{1 - \cos 5x}{\sin 3x}$?

Published on 10 Feb 2024 - 9:48

List Question

The value of $\lim_{h\to 0}\frac{\sin(a+3h)-3\sin(a+2h)+3\sin(a+h)-\sin a}{h^3}$ is?

Limit of a function with an integral to have a variable in the upper bound

Please identify my mistake: $\lim_{h\to0}\frac{\ln (1+2 h)-2 \ln (1+h)}{h^2}$

Does $\lim_{x \to 1}\left(\frac{x}{[x]}\right)$ exist?

Find $\lim\limits_{x \to 0} \frac{ \sqrt{1+x} - 1} { \sqrt[3]{1+x} - 1}$.

Calculating limit of a function without using L'Hospital

Evaluating $\lim_{x\to 1}\frac{8^x-8}{x-1}$ without using L'Hopital rule

This limit is puzzling me

Nonanalytic function with Taylor series of all orders

If $\lim\limits_{x\to0}f(x)=0$ and $\lim\limits_{x \to 0}\frac{f(2x)-f(x)}{x}=0$ how to rigorously prove that $\lim\limits_{x \to 0}\frac{f(x)}{x}=0$?

With $x_1=1$ and $x_{n+1} = \frac{1}{x_1^2+x_2^2+\dots+x_{n}^2}$show$\lim\limits_{n\to\infty}\frac{x_1+x_2+\dots+x_n}{n^{2/3}}=\frac{\sqrt[3]{9}}{2}$

How to solve this limit without using L'Hopital

$\lim_{x \rightarrow 0} \frac{(x^2 - x^3) ((x + 1)^\sqrt{2} - 1)}{\log(1 + 4 x) (1 - \cos(2 x))}$

A limit of $1^\infty$ form (maybe)

Without using L'Hopitals rule, how do you get $\lim_{x \to 0} \frac{1 - \cos 5x}{\sin 3x}$?

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