Question

If ${\lim_{x \to a}} f(x)=L$ then ${\lim_{x \to a}}\sqrt[n]{f(x)}=\sqrt[n]L$

score 129 · Answer 1 · 2026-03-25 17:41:51

129

Views

If ${\lim_{x \to a}} f(x)=L$ then ${\lim_{x \to a}}\sqrt[n]{f(x)}=\sqrt[n]L$

Published on 25 Mar 2026 - 17:41

score 91 · Answer 2 · 2019-02-27 04:43:01

91

Views

Does the following limit exist $\lim_{x \to 0} \frac{\cos x^{-2}}{ \cos x^{-2}}$

Published on 27 Feb 2019 - 4:43

score 40 · Answer 3 · 2019-02-28 16:41:38

40

Views

Proof Verification: Show that $f(x,y)=\frac{x^2\sin(xy)}{\sqrt{x^2+y^2}}$ is continuous on $\mathbb{R}^2$

Published on 28 Feb 2019 - 16:41

score 252 · Answer 4 · 2019-03-01 03:12:06

252

Views

Give a $\delta$-$\varepsilon$ proof that $f(x,y)=\sqrt{x+y-2}$ is continuous at $(2,1)$.

Published on 01 Mar 2019 - 3:12

score 166 · Answer 5 · 2019-03-02 13:55:16

166

Views

Prove $\lim_{x \to 2} \frac{x+1}{x+2}=\frac{3}{4}$ using the epsilon delta definition of the limit.

Published on 02 Mar 2019 - 13:55

score 69 · Answer 6 · 2019-03-03 15:43:59

69

Views

Link between $f$ and $f'$

Published on 03 Mar 2019 - 15:43

score 198 · Answer 7 · 2019-03-03 20:23:00

198

Views

Is it possible for $x$ to appear in the definition of $\delta$ in an $\epsilon-\delta$ proof of limit?

Published on 03 Mar 2019 - 20:23

score 213 · Answer 8 · 2019-03-04 21:50:29

213

Views

Let $f$ be a function from a metric space to a metric space. Prove that $f$ is continuous i.f.f it sends convergent sequences into convergent seq.

Published on 04 Mar 2019 - 21:50

score 31 · Answer 9 · 2019-03-04 22:49:04

31

Views

Showing |f(x)-f(y)| < $(\frac1\epsilon)^2*|x-y|$ for x,y on [$\epsilon^3/4,1$]

Published on 04 Mar 2019 - 22:49

score 418 · Answer 10 · 2019-03-05 00:27:50

418

Views

Prove that $\lim\limits_{(x,y)\to (0,0)} \frac{\sin(xy)}{\sin(x)\sin(y)}$ exists, using $(\epsilon ,\delta)$-argument

Published on 05 Mar 2019 - 0:27

score 61 · Answer 11 · 2019-03-05 20:20:45

Prove that $\lim_{\left( u, v \right) \rightarrow \left( 0, 0 \right)} \frac{u}{\sqrt{v+4}} = 0$ using the $\epsilon - \delta$ definition

score 45 · Answer 12 · 2019-03-11 16:42:02

45

Views

proof lim x-a f(x)= lim x-0 f(x+a) ( duplicate)

Published on 11 Mar 2019 - 16:42

score 83 · Answer 13 · 2019-03-11 17:39:30

83

Views

Intuitive explanation of sign preservation of limits and boundedness?

Published on 11 Mar 2019 - 17:39

score 170 · Answer 14 · 2019-03-12 15:53:22

170

Views

Question about the proof of the $\epsilon-\delta$ definition of continuity

Published on 12 Mar 2019 - 15:53

score 91 · Answer 15 · 2019-03-13 10:40:37

Using the $\varepsilon − N$ definition of the limit, prove that $\lim \limits_{n\to\infty} \frac{(n^2 + 1)}{ (n^2 + 2)} = 1$.

List Question

If ${\lim_{x \to a}} f(x)=L$ then ${\lim_{x \to a}}\sqrt[n]{f(x)}=\sqrt[n]L$

Does the following limit exist $\lim_{x \to 0} \frac{\cos x^{-2}}{ \cos x^{-2}}$

Proof Verification: Show that $f(x,y)=\frac{x^2\sin(xy)}{\sqrt{x^2+y^2}}$ is continuous on $\mathbb{R}^2$

Give a $\delta$-$\varepsilon$ proof that $f(x,y)=\sqrt{x+y-2}$ is continuous at $(2,1)$.

Prove $\lim_{x \to 2} \frac{x+1}{x+2}=\frac{3}{4}$ using the epsilon delta definition of the limit.

Link between $f$ and $f'$

Is it possible for $x$ to appear in the definition of $\delta$ in an $\epsilon-\delta$ proof of limit?

Let $f$ be a function from a metric space to a metric space. Prove that $f$ is continuous i.f.f it sends convergent sequences into convergent seq.

Showing |f(x)-f(y)| < $(\frac1\epsilon)^2*|x-y|$ for x,y on [$\epsilon^3/4,1$]

Prove that $\lim\limits_{(x,y)\to (0,0)} \frac{\sin(xy)}{\sin(x)\sin(y)}$ exists, using $(\epsilon ,\delta)$-argument

Prove that $\lim_{\left( u, v \right) \rightarrow \left( 0, 0 \right)} \frac{u}{\sqrt{v+4}} = 0$ using the $\epsilon - \delta$ definition

proof lim x-a f(x)= lim x-0 f(x+a) ( duplicate)

Intuitive explanation of sign preservation of limits and boundedness?

Question about the proof of the $\epsilon-\delta$ definition of continuity

Using the $\varepsilon − N$ definition of the limit, prove that $\lim \limits_{n\to\infty} \frac{(n^2 + 1)}{ (n^2 + 2)} = 1$.

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