Question

Prove $\lim_{n\to\infty} \frac{n^2 + n + 1} {2n^2 - 4}= 1/2$ by definition

score 60 · Answer 1 · 2021-10-06 10:56:24

60

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Prove $\lim_{n\to\infty} \frac{n^2 + n + 1} {2n^2 - 4}= 1/2$ by definition

Published on 06 Oct 2021 - 10:56

score 91 · Answer 2 · 2021-10-06 16:34:11

91

Views

Use the $\epsilon$-$\delta$ definition to prove the following limit

Published on 06 Oct 2021 - 16:34

score 58 · Answer 3 · 2021-10-07 12:59:03

58

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Use the $\varepsilon - \delta$ definition of the limit to verify that $\lim_{(x,y)\to(2,5)} xy = 10$

Published on 07 Oct 2021 - 12:59

score 274 · Answer 4 · 2021-10-07 23:12:25

274

Views

Prove (by definition) that $\lim _{z\to 1+i}\left(\frac{1}{z^2+1}\right)=\frac{1}{2i+1}$

Published on 07 Oct 2021 - 23:12

score 126 · Answer 5 · 2021-10-08 01:29:17

126

Views

Proof for a limit - Epsilon-delta proof $3x^2 +2x +4$

Published on 08 Oct 2021 - 1:29

score 98 · Answer 6 · 2021-10-08 08:09:51

98

Views

$\lim_{x \to0} \frac{f(bx)}{bx} = \lim_{x \to 0} \frac{f(x)}{x}$ proof verification

Published on 08 Oct 2021 - 8:09

score 69 · Answer 7 · 2021-10-10 23:15:17

69

Views

Use $\varepsilon$-$N$ definition of convergence to show $\lim (1+\frac{1}{n})^2 = 1$

Published on 10 Oct 2021 - 23:15

score 53 · Answer 8 · 2021-10-11 17:43:33

53

Views

Determining the "perfect" $\delta$ in the uniform continuity of $\sqrt[3]{1-x^2}$

Published on 11 Oct 2021 - 17:43

score 48 · Answer 9 · 2021-10-13 00:07:22

48

Views

When proving limits, If I get $0<|f(x)-L|<10\epsilon$

Published on 13 Oct 2021 - 0:07

score 50 · Answer 10 · 2021-10-15 03:47:36

50

Views

$\epsilon$-$\delta$ Proof: prove $\lim_{x\to 0} f(\sin(x)+1) = 5$, if $\lim_{x\to 1}f(x)=5$

Published on 15 Oct 2021 - 3:47

score 257 · Answer 11 · 2021-10-17 16:26:55

257

Views

Proving limits by $\epsilon-\delta$ in vector-valued several-variable functions

Published on 17 Oct 2021 - 16:26

score 104 · Answer 12 · 2021-10-17 17:41:04

104

Views

Epsilon delta proof of a quadratic reciprocal

Published on 17 Oct 2021 - 17:41

score 1.1k · Answer 13 · 2021-10-18 20:00:21

1.1k

Views

Find $\delta > 0$ such that $|x-2| < \delta$ implies $|x^2+2x-18| < \frac{1}{4}$

Published on 18 Oct 2021 - 20:00

score 158 · Answer 14 · 2021-10-19 22:11:44

158

Views

$\delta$-$\epsilon$ Proof: Prove $\lim_{x\to{a}}f(x)=\infty\implies\lim_{x\to{a}}f(x)$ does not exist, using the formal definition of the limit

Published on 19 Oct 2021 - 22:11

score 201 · Answer 15 · 2021-10-20 23:42:43

201

Views

Prove that $\ln(x)$ is uniformly continuous on the set $[1,\infty)$

Published on 20 Oct 2021 - 23:42

List Question

Prove $\lim_{n\to\infty} \frac{n^2 + n + 1} {2n^2 - 4}= 1/2$ by definition

Use the $\epsilon$-$\delta$ definition to prove the following limit

Use the $\varepsilon - \delta$ definition of the limit to verify that $\lim_{(x,y)\to(2,5)} xy = 10$

Prove (by definition) that $\lim _{z\to 1+i}\left(\frac{1}{z^2+1}\right)=\frac{1}{2i+1}$

Proof for a limit - Epsilon-delta proof $3x^2 +2x +4$

$\lim_{x \to0} \frac{f(bx)}{bx} = \lim_{x \to 0} \frac{f(x)}{x}$ proof verification

Use $\varepsilon$-$N$ definition of convergence to show $\lim (1+\frac{1}{n})^2 = 1$

Determining the "perfect" $\delta$ in the uniform continuity of $\sqrt[3]{1-x^2}$

When proving limits, If I get $0<|f(x)-L|<10\epsilon$

$\epsilon$-$\delta$ Proof: prove $\lim_{x\to 0} f(\sin(x)+1) = 5$, if $\lim_{x\to 1}f(x)=5$

Proving limits by $\epsilon-\delta$ in vector-valued several-variable functions

Epsilon delta proof of a quadratic reciprocal

Find $\delta > 0$ such that $|x-2| < \delta$ implies $|x^2+2x-18| < \frac{1}{4}$

$\delta$-$\epsilon$ Proof: Prove $\lim_{x\to{a}}f(x)=\infty\implies\lim_{x\to{a}}f(x)$ does not exist, using the formal definition of the limit

Prove that $\ln(x)$ is uniformly continuous on the set $[1,\infty)$

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