Question

Calculate $\lim_{n \rightarrow \infty } \frac{n (1- na_n)}{\log n} $

score 668 · Answer 1 · 2026-04-19 01:52:53

668

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Calculate $\lim_{n \rightarrow \infty } \frac{n (1- na_n)}{\log n} $

Published on 19 Apr 2026 - 1:52

score 129 · Answer 2 · 2026-05-14 21:28:47

129

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Limits for sequences: Prove that $\lim_{n \rightarrow \infty} \frac{2n^2 - 3n + 5}{9 - n^2} = -2$

Published on 14 May 2026 - 21:28

score 824 · Answer 3 · 2026-04-11 22:43:43

824

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L'Hopital's rule $\infty-\infty$

Published on 11 Apr 2026 - 22:43

score 194 · Answer 4 · 2026-04-16 00:44:03

194

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Value of $\lim_{n \to \infty} \left({\frac{(n+1)(n+2)(n+3)...(3n)}{n{^{2n}}}}\right)^{1/n}$

Published on 16 Apr 2026 - 0:44

score 58 · Answer 5 · 2026-04-16 03:08:14

58

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Show that $\displaystyle\lim_{x \rightarrow 0^{+}} f(x) = f(0)$

Published on 16 Apr 2026 - 3:08

score 151 · Answer 6 · 2026-04-17 07:08:15

151

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What can we say about $\lim_{n\rightarrow\infty}\int_0^\infty \frac{\sin(x^n)}{x^n}\,dx$?

Published on 17 Apr 2026 - 7:08

score 57 · Answer 7 · 2026-04-16 08:58:57

57

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$\lim_{(x,y) \to (0,0)}\frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}} = 0 \Longleftrightarrow \frac{a}{c} + \frac{b}{d} > 1$

Published on 16 Apr 2026 - 8:58

score 286 · Answer 8 · 2026-05-11 00:47:10

286

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Powers of Irreducible Polynomials in Partial Fractions

Published on 11 May 2026 - 0:47

score 349 · Answer 9 · 2026-05-10 15:01:46

349

Views

limit of sequence involving the fractional part

Published on 10 May 2026 - 15:01

score 58 · Answer 10 · 2026-04-16 03:37:31

58

Views

the probability that a limit works out to zero

Published on 16 Apr 2026 - 3:37

score 39 · Answer 11 · 2026-04-14 09:46:21

39

Views

Limit of a quotient.

Published on 14 Apr 2026 - 9:46

score 352 · Answer 12 · 2026-04-17 03:01:56

352

Views

Solving limits that approach infinity

Published on 17 Apr 2026 - 3:01

score 517 · Answer 13 · 2026-05-10 13:46:59

517

Views

Continuity and differentiability of elementary functions

Published on 10 May 2026 - 13:46

score 173 · Answer 14 · 2026-05-11 01:54:43

173

Views

Sufficient condition to show that f(x) is monotonic in some neighbourhood of x

Published on 11 May 2026 - 1:54

score 123 · Answer 15 · 2026-04-15 17:56:37

If $f : [a, \infty) → \Bbb R$ is monotonically decreasing and the integral $\int_0^\infty f(x) \,dx$ is convergent, then $\lim_{x→\infty} f(x) = 0$.

List Question

Calculate $\lim_{n \rightarrow \infty } \frac{n (1- na_n)}{\log n} $

Limits for sequences: Prove that $\lim_{n \rightarrow \infty} \frac{2n^2 - 3n + 5}{9 - n^2} = -2$

L'Hopital's rule $\infty-\infty$

Value of $\lim_{n \to \infty} \left({\frac{(n+1)(n+2)(n+3)...(3n)}{n{^{2n}}}}\right)^{1/n}$

Show that $\displaystyle\lim_{x \rightarrow 0^{+}} f(x) = f(0)$

What can we say about $\lim_{n\rightarrow\infty}\int_0^\infty \frac{\sin(x^n)}{x^n}\,dx$?

$\lim_{(x,y) \to (0,0)}\frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}} = 0 \Longleftrightarrow \frac{a}{c} + \frac{b}{d} > 1$

Powers of Irreducible Polynomials in Partial Fractions

limit of sequence involving the fractional part

the probability that a limit works out to zero

Limit of a quotient.

Solving limits that approach infinity

Continuity and differentiability of elementary functions

Sufficient condition to show that f(x) is monotonic in some neighbourhood of x

If $f : [a, \infty) → \Bbb R$ is monotonically decreasing and the integral $\int_0^\infty f(x) \,dx$ is convergent, then $\lim_{x→\infty} f(x) = 0$.

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