Question

Prove $\frac{\sqrt{x}}{x-1}$ is continuous on (0,1)

score 167 · Answer 1 · 2026-04-13 12:07:07

167

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Prove $\frac{\sqrt{x}}{x-1}$ is continuous on (0,1)

Published on 13 Apr 2026 - 12:07

score 1.4k · Answer 2 · 2026-05-10 21:13:41

1.4k

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Limits and While Loops

Published on 10 May 2026 - 21:13

score 79 · Answer 3 · 2026-04-16 10:10:06

79

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Define $f$ on $[0, 4]$ by $f(x) = x+ 1$ for $0 ≤ x < 2$ and $f(x) = 1$ for $2 ≤ x ≤ 4$. Use the extreme value theorem to show that f is not continuous

Published on 16 Apr 2026 - 10:10

score 118 · Answer 4 · 2026-04-16 01:16:33

118

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Find $\lim_{x\to0}\frac{\sin4x}{x^2+x}$

Published on 16 Apr 2026 - 1:16

score 248 · Answer 5 · 2026-04-16 17:25:02

248

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Find $\lim_{x\rightarrow 0} \frac{5^x-3^x}{3^x-2^x}$

Published on 16 Apr 2026 - 17:25

score 360 · Answer 6 · 2026-05-11 00:33:19

360

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How can I proof that a circle's circumference is well defined? And How do I find it?

Published on 11 May 2026 - 0:33

score 45 · Answer 7 · 2026-04-12 13:39:26

45

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Limit of Function

Published on 12 Apr 2026 - 13:39

score 110 · Answer 8 · 2026-04-15 22:11:52

110

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How to find $a$ and $b$ in $\lim\limits_{x→0}\frac{\sqrt{ax+b}-2}{x}=1$?

Published on 15 Apr 2026 - 22:11

score 109 · Answer 9 · 2026-04-13 14:25:58

109

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How to show $\int_x ^\infty f(t)dt \to 0$ as $x\to \infty$

Published on 13 Apr 2026 - 14:25

score 2.5k · Answer 10 · 2026-04-16 11:53:35

2.5k

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Prove $\frac{d}{dx} x^n=nx^{n-1} : \forall n\in \mathbb{Z}_{+}$ by induction

Published on 16 Apr 2026 - 11:53

score 438 · Answer 11 · 2026-04-14 17:44:53

438

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Using L'Hôpital's rule on $\lim_{x \to 0}(xe^{\frac{1}{x}}-x) $

Published on 14 Apr 2026 - 17:44

score 118 · Answer 12 · 2026-05-14 03:45:28

118

Views

Rational limit on two variables approaching the origin

Published on 14 May 2026 - 3:45

score 118 · Answer 13 · 2026-04-15 00:09:09

118

Views

$\ \lim_{x\to0} \frac{x}{\cos(\frac{\pi}{2}-x)} $ without L'Hospital's rule

Published on 15 Apr 2026 - 0:09

score 73 · Answer 14 · 2026-05-10 12:51:19

73

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Does the limit exist ? and how to compute it?

Published on 10 May 2026 - 12:51

score 22 · Answer 15 · 2026-04-15 18:42:27

22

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I alphabetize a large number of two-letter words. What is the expected ratio of words starting with A to words starting with B?

Published on 15 Apr 2026 - 18:42

List Question

Prove $\frac{\sqrt{x}}{x-1}$ is continuous on (0,1)

Limits and While Loops

Define $f$ on $[0, 4]$ by $f(x) = x+ 1$ for $0 ≤ x < 2$ and $f(x) = 1$ for $2 ≤ x ≤ 4$. Use the extreme value theorem to show that f is not continuous

Find $\lim_{x\to0}\frac{\sin4x}{x^2+x}$

Find $\lim_{x\rightarrow 0} \frac{5^x-3^x}{3^x-2^x}$

How can I proof that a circle's circumference is well defined? And How do I find it?

Limit of Function

How to find $a$ and $b$ in $\lim\limits_{x→0}\frac{\sqrt{ax+b}-2}{x}=1$?

How to show $\int_x ^\infty f(t)dt \to 0$ as $x\to \infty$

Prove $\frac{d}{dx} x^n=nx^{n-1} : \forall n\in \mathbb{Z}_{+}$ by induction

Using L'Hôpital's rule on $\lim_{x \to 0}(xe^{\frac{1}{x}}-x) $

Rational limit on two variables approaching the origin

$\ \lim_{x\to0} \frac{x}{\cos(\frac{\pi}{2}-x)} $ without L'Hospital's rule

Does the limit exist ? and how to compute it?

I alphabetize a large number of two-letter words. What is the expected ratio of words starting with A to words starting with B?

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