Question

Limit of a weighted sum raised to a power

score 189 · Answer 1 · 2026-05-10 20:40:48

189

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Limit of a weighted sum raised to a power

Published on 10 May 2026 - 20:40

score 239 · Answer 2 · 2026-04-14 18:26:31

239

Views

$\lim_{n\to\infty}n^2\int_0^1x^nf(x)dx$ if $f(1)=0$

Published on 14 Apr 2026 - 18:26

score 38 · Answer 3 · 2026-05-14 11:32:49

38

Views

Proof sequence converges with monotonocity and boundedness of subsequences without induction?

Published on 14 May 2026 - 11:32

score 260 · Answer 4 · 2026-05-11 01:48:35

260

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Does $f(x)=x \ln (x)$ have a vertical tangent

Published on 11 May 2026 - 1:48

score 70 · Answer 5 · 2026-04-29 19:15:39

70

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Doubt in proof of Rolle's Theorem

Published on 29 Apr 2026 - 19:15

score 90 · Answer 6 · 2026-04-11 11:14:56

90

Views

Limits in a normed space

Published on 11 Apr 2026 - 11:14

score 157 · Answer 7 · 2026-04-17 09:46:37

157

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Prove ${\lim\limits_{m \to +\infty}} \ln{\left(1+\frac{r}{m}\right)} = \frac{r}{m}$

Published on 17 Apr 2026 - 9:46

score 118 · Answer 8 · 2026-04-15 22:29:19

Find: $\lim_{n\longrightarrow\infty}\left(\frac{f(a+\frac{1}{n})}{f(a)}\right)^{n}$ as $f$ is differentiable on $x=a$, and $f'(a)=2, f(a)=5$

score 96 · Answer 9 · 2026-04-09 15:24:56

96

Views

Prove that $\lim \limits_{n\to \infty}\int_{n}^{\infty} f_{n}(x)dx\neq \int_{n}^{\infty} f(x)dx $

Published on 09 Apr 2026 - 15:24

score 254 · Answer 10 · 2026-04-16 11:05:14

254

Views

Finding $\delta $ for $\lim_{x \to 0} x \ [3-\cos(x^2)] = 0 $

Published on 16 Apr 2026 - 11:05

score 132 · Answer 11 · 2026-04-16 03:10:50

132

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How do you evaluate limit of $\frac{\sqrt{1+x^2} - \sqrt {1+x}}{\sqrt {1+x^3} - \sqrt {{1+x}}}$ when $x$ tends to $0$?

Published on 16 Apr 2026 - 3:10

score 117 · Answer 12 · 2026-04-11 00:11:51

117

Views

Why does the definition of convergence have $<\varepsilon$ instead of $\le\varepsilon$?

Published on 11 Apr 2026 - 0:11

score 32 · Answer 13 · 2026-04-17 14:20:36

32

Views

Alternative way to solve a rational limit in $\Bbb C$ when factorization and denominator conjugation fail

Published on 17 Apr 2026 - 14:20

score 80 · Answer 14 · 2026-04-14 22:17:09

80

Views

A question about $\lim_{n\to\infty} \left(n-\sum_{k=1}^n e^{\frac{k}{n^2}}\right)$

Published on 14 Apr 2026 - 22:17

score 66 · Answer 15 · 2026-05-10 16:35:48

66

Views

Show that $\lim_{t \to \infty} \sup_{x \ge 0} \frac{1}{x^2+1} e^{-x} \sum_{n>t} \frac{n x^{n}}{n!}=0$

Published on 10 May 2026 - 16:35

List Question

Limit of a weighted sum raised to a power

$\lim_{n\to\infty}n^2\int_0^1x^nf(x)dx$ if $f(1)=0$

Proof sequence converges with monotonocity and boundedness of subsequences without induction?

Does $f(x)=x \ln (x)$ have a vertical tangent

Doubt in proof of Rolle's Theorem

Limits in a normed space

Prove ${\lim\limits_{m \to +\infty}} \ln{\left(1+\frac{r}{m}\right)} = \frac{r}{m}$

Find: $\lim_{n\longrightarrow\infty}\left(\frac{f(a+\frac{1}{n})}{f(a)}\right)^{n}$ as $f$ is differentiable on $x=a$, and $f'(a)=2, f(a)=5$

Prove that $\lim \limits_{n\to \infty}\int_{n}^{\infty} f_{n}(x)dx\neq \int_{n}^{\infty} f(x)dx $

Finding $\delta $ for $\lim_{x \to 0} x \ [3-\cos(x^2)] = 0 $

How do you evaluate limit of $\frac{\sqrt{1+x^2} - \sqrt {1+x}}{\sqrt {1+x^3} - \sqrt {{1+x}}}$ when $x$ tends to $0$?

Why does the definition of convergence have $<\varepsilon$ instead of $\le\varepsilon$?

Alternative way to solve a rational limit in $\Bbb C$ when factorization and denominator conjugation fail

A question about $\lim_{n\to\infty} \left(n-\sum_{k=1}^n e^{\frac{k}{n^2}}\right)$

Show that $\lim_{t \to \infty} \sup_{x \ge 0} \frac{1}{x^2+1} e^{-x} \sum_{n>t} \frac{n x^{n}}{n!}=0$

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