Question

Using the sequential definition of a limit to show $\lim_{x\to 1} \frac{x^2 - 1}{\sqrt{x} - 1} = 4.$

score 818 · Answer 1 · 2026-04-16 12:18:55

818

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Using the sequential definition of a limit to show $\lim_{x\to 1} \frac{x^2 - 1}{\sqrt{x} - 1} = 4.$

Published on 16 Apr 2026 - 12:18

score 47 · Answer 2 · 2026-04-15 02:42:17

47

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Convergence of series and limit

Published on 15 Apr 2026 - 2:42

score 64 · Answer 3 · 2026-04-11 22:39:14

64

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Finding limit without using the l'Hopital theorem

Published on 11 Apr 2026 - 22:39

score 51 · Answer 4 · 2026-04-17 15:48:08

51

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Limit without l'Hopital and using another one.

Published on 17 Apr 2026 - 15:48

score 100 · Answer 5 · 2026-04-17 02:47:45

100

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Evaluate $\lim\limits_{x \to +\infty}\left[\sqrt[4]{x^4+x^3+x^2+x+1}-\sqrt[3]{x^3+x^2+x+1}\cdot \frac{\ln(x+e^x)}{x}\right].$

Published on 17 Apr 2026 - 2:47

score 47 · Answer 6 · 2026-04-14 11:22:33

47

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Where is the mistake in finding $c$ and $n$ of $\sqrt{x^3+4x} - \sqrt{x^3+x} \sim cx^n$ for $x \to 0$ and $x \to +\infty$

Published on 14 Apr 2026 - 11:22

score 39 · Answer 7 · 2026-04-16 08:59:57

Limit of the $r$-norm $(\sum_{i=0}^n (y_1,x_i)-(y_2,x_i))^r )^{1/r}$ as $r \to \infty$ is $ \max_i \left|(y_1,x_i)-(y_2,x_i)\right| $

score 550 · Answer 8 · 2026-05-10 23:31:39

550

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Prove that $\lim_{n \to \infty} \sup (x_n) =\min\{A \in \Bbb{R} : \forall\epsilon>0 \{n \in \mathbb{N}: x_n \geq A+ \epsilon \} $ set is finite}

Published on 10 May 2026 - 23:31

score 13.4k · Answer 9 · 2026-04-10 19:47:00

13.4k

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What is the limit of zero times x, as x approaches infinity?

Published on 10 Apr 2026 - 19:47

score 1.5k · Answer 10 · 2026-04-15 20:11:44

1.5k

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Proof that the sequence $\left\{\frac{5n^2-6}{2n^3-7n}\right\}$ converges to $0$

Published on 15 Apr 2026 - 20:11

score 47 · Answer 11 · 2026-04-09 20:10:45

47

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Checking series for convergence and limit

Published on 09 Apr 2026 - 20:10

score 245 · Answer 12 · 2026-04-17 08:45:56

245

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Is there a non alternating sequence that diverges but converges when squared?

Published on 17 Apr 2026 - 8:45

score 51 · Answer 13 · 2026-04-14 00:26:20

51

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Prove convergence of limit in $\mathbb{R}$.

Published on 14 Apr 2026 - 0:26

score 1.8k · Answer 14 · 2026-04-16 22:30:03

1.8k

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Limit of harmonic series

Published on 16 Apr 2026 - 22:30

score 144 · Answer 15 · 2026-05-11 03:17:46

144

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Finding the limit of the sequence $(1, \frac{1}{2+1}, \frac{1}{2+\frac{1}{1+1}},\cdots)$

Published on 11 May 2026 - 3:17

List Question

Using the sequential definition of a limit to show $\lim_{x\to 1} \frac{x^2 - 1}{\sqrt{x} - 1} = 4.$

Convergence of series and limit

Finding limit without using the l'Hopital theorem

Limit without l'Hopital and using another one.

Evaluate $\lim\limits_{x \to +\infty}\left[\sqrt[4]{x^4+x^3+x^2+x+1}-\sqrt[3]{x^3+x^2+x+1}\cdot \frac{\ln(x+e^x)}{x}\right].$

Where is the mistake in finding $c$ and $n$ of $\sqrt{x^3+4x} - \sqrt{x^3+x} \sim cx^n$ for $x \to 0$ and $x \to +\infty$

Limit of the $r$-norm $(\sum_{i=0}^n (y_1,x_i)-(y_2,x_i))^r )^{1/r}$ as $r \to \infty$ is $ \max_i \left|(y_1,x_i)-(y_2,x_i)\right| $

Prove that $\lim_{n \to \infty} \sup (x_n) =\min\{A \in \Bbb{R} : \forall\epsilon>0 \{n \in \mathbb{N}: x_n \geq A+ \epsilon \} $ set is finite}

What is the limit of zero times x, as x approaches infinity?

Proof that the sequence $\left\{\frac{5n^2-6}{2n^3-7n}\right\}$ converges to $0$

Checking series for convergence and limit

Is there a non alternating sequence that diverges but converges when squared?

Prove convergence of limit in $\mathbb{R}$.

Limit of harmonic series

Finding the limit of the sequence $(1, \frac{1}{2+1}, \frac{1}{2+\frac{1}{1+1}},\cdots)$

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