Question

Limits of two variables $\lim_{t \rightarrow \infty} \lim_{u \rightarrow t} u^{\alpha} \sqrt{t-u} = 0$

score 36 · Answer 1 · 2026-04-16 09:28:11

36

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Limits of two variables $\lim_{t \rightarrow \infty} \lim_{u \rightarrow t} u^{\alpha} \sqrt{t-u} = 0$

Published on 16 Apr 2026 - 9:28

score 55 · Answer 2 · 2026-04-17 14:20:07

55

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Let $f(x)=x$ for $x\in [0,1]$ Then show $\lim _{n\rightarrow \infty } L(f,P_n)=\lim _{n\rightarrow \infty } U(f,P_n)=\dfrac {1} {2}$

Published on 17 Apr 2026 - 14:20

score 103 · Answer 3 · 2026-04-14 09:19:20

103

Views

Proof for: $x \in \overline{A} \iff (x_n)_n$ exists in $A$ with $x_n \to x$

Published on 14 Apr 2026 - 9:19

score 73 · Answer 4 · 2026-04-15 14:42:32

73

Views

Show that $f(z) = 5\sin(z) - \exp(z)$ has exactly one zero in a region.

Published on 15 Apr 2026 - 14:42

score 7k · Answer 5 · 2026-04-12 23:32:35

7k

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Example of a metric space first countable but not second countable.

Published on 12 Apr 2026 - 23:32

score 209 · Answer 6 · 2026-04-13 22:43:03

209

Views

Convergence of an improper integral of two variables

Published on 13 Apr 2026 - 22:43

score 648 · Answer 7 · 2026-04-14 05:35:15

648

Views

Question on Baby Rudin 1.22 about decimal expansions

Published on 14 Apr 2026 - 5:35

score 90 · Answer 8 · 2026-04-14 16:37:27

90

Views

Limit $\lim_{n \to \infty} \frac{n!}{n^n}$

Published on 14 Apr 2026 - 16:37

score 240 · Answer 9 · 2026-04-15 16:29:59

240

Views

Prove that finite linear combination of $x^n$ is dense in $L^2 ([0,1]) $

Published on 15 Apr 2026 - 16:29

score 68 · Answer 10 · 2026-04-14 04:53:04

68

Views

function $f$ is continuous in $[0,\infty)$ and $\displaystyle\lim_{x \to \infty} f(x) = f(0)$, prove that $f$ is not injective in $[0,\infty)$

Published on 14 Apr 2026 - 4:53

score 102 · Answer 11 · 2026-04-11 21:05:42

102

Views

Necessary condition for an improper integral of two variables to converge

Published on 11 Apr 2026 - 21:05

score 3k · Answer 12 · 2026-04-15 18:02:41

3k

Views

Find derivatives with respect to parameter or initial condition

Published on 15 Apr 2026 - 18:02

score 143 · Answer 13 · 2026-04-12 10:42:30

143

Views

Find limit distribution of given random variable

Published on 12 Apr 2026 - 10:42

score 358 · Answer 14 · 2026-04-15 14:43:50

358

Views

Arzela Ascoli Theorem for compactness of a set

Published on 15 Apr 2026 - 14:43

score 49 · Answer 15 · 2026-04-15 21:51:49

49

Views

Positive Integer Multiple of Convergent, Decreasing Sequence Can Be Made Arbitrarily Small

Published on 15 Apr 2026 - 21:51

List Question

Limits of two variables $\lim_{t \rightarrow \infty} \lim_{u \rightarrow t} u^{\alpha} \sqrt{t-u} = 0$

Let $f(x)=x$ for $x\in [0,1]$ Then show $\lim _{n\rightarrow \infty } L(f,P_n)=\lim _{n\rightarrow \infty } U(f,P_n)=\dfrac {1} {2}$

Proof for: $x \in \overline{A} \iff (x_n)_n$ exists in $A$ with $x_n \to x$

Show that $f(z) = 5\sin(z) - \exp(z)$ has exactly one zero in a region.

Example of a metric space first countable but not second countable.

Convergence of an improper integral of two variables

Question on Baby Rudin 1.22 about decimal expansions

Limit $\lim_{n \to \infty} \frac{n!}{n^n}$

Prove that finite linear combination of $x^n$ is dense in $L^2 ([0,1]) $

function $f$ is continuous in $[0,\infty)$ and $\displaystyle\lim_{x \to \infty} f(x) = f(0)$, prove that $f$ is not injective in $[0,\infty)$

Necessary condition for an improper integral of two variables to converge

Find derivatives with respect to parameter or initial condition

Find limit distribution of given random variable

Arzela Ascoli Theorem for compactness of a set

Positive Integer Multiple of Convergent, Decreasing Sequence Can Be Made Arbitrarily Small

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