Question

Examine whether $\sum_{n=1}^\infty{\sin^2\left(\frac{1}{n}\right)}$ converges or not

score 198 · Answer 1 · 2026-04-16 08:18:15

198

Views

Examine whether $\sum_{n=1}^\infty{\sin^2\left(\frac{1}{n}\right)}$ converges or not

Published on 16 Apr 2026 - 8:18

score 87 · Answer 2 · 2026-04-16 16:17:02

87

Views

Evaluate $\lim_{(x,y,z)\to (0,0,0)}\frac{1}{x^2+y^2+z^2}e^{-\frac{1}{\sqrt{x^2+y^2+z^2}}}$

Published on 16 Apr 2026 - 16:17

score 1.2k · Answer 3 · 2026-04-14 19:44:16

1.2k

Views

Given any non-real, complex number with positive real part, must some power of it has negative real part?

Published on 14 Apr 2026 - 19:44

score 53 · Answer 4 · 2026-04-18 09:19:28

For what $\alpha$ and $\beta$ values does $\lim_{(x,y)\to (0,0)}$ $\frac {| x|^{\alpha}| y|^{\beta}}{\ x^4 + y^4 }$ goes to $0$?

score 173 · Answer 5 · 2026-05-11 01:00:54

173

Views

Integrate indefinite integral

Published on 11 May 2026 - 1:00

score 60 · Answer 6 · 2026-04-16 20:00:25

60

Views

Evaluate $\lim_{h\to 0}\frac{1}{h^3e^{\frac{1}{\sqrt{h^2}}}}$

Published on 16 Apr 2026 - 20:00

score 40 · Answer 7 · 2026-05-14 18:21:31

40

Views

Continuity and close map . [Metric Space.]

Published on 14 May 2026 - 18:21

score 159 · Answer 8 · 2026-05-10 14:55:52

159

Views

Proving uniform continuity of the exponential function on a semi-finite interval

Published on 10 May 2026 - 14:55

score 453 · Answer 9 · 2026-05-11 01:53:15

453

Views

Prove that a metric space $S$ is disconnected iff $\exists$ a non empty subset $A$ of $S$ s.t. $A \neq S$ and $A$ is both open and closed.

Published on 11 May 2026 - 1:53

score 131 · Answer 10 · 2026-05-13 16:13:08

131

Views

Are points negligible for weak derivative in dimension 2?

Published on 13 May 2026 - 16:13

score 217 · Answer 11 · 2026-04-14 15:32:53

217

Views

Proving that the counting measure is a measure on $\mathcal A$

Published on 14 Apr 2026 - 15:32

score 72 · Answer 12 · 2026-05-14 18:21:23

72

Views

Metric Space (Continuity)

Published on 14 May 2026 - 18:21

score 1k · Answer 13 · 2026-05-15 09:35:41

1k

Views

How to prove that $L^{\infty}([0,1]) \subset L^q([0,1]) \subset L^p([0,1])$?

Published on 15 May 2026 - 9:35

score 296 · Answer 14 · 2026-04-13 13:06:24

296

Views

Pointwise a.e. convergence vs. Pointwise convergence

Published on 13 Apr 2026 - 13:06

score 1.7k · Answer 15 · 2026-05-15 05:31:38

1.7k

Views

Prove that $f(x,y) = \sqrt{x^2 + y^2}$ is continuous at $a=(3,\frac{1}{2})$

Published on 15 May 2026 - 5:31

List Question

Examine whether $\sum_{n=1}^\infty{\sin^2\left(\frac{1}{n}\right)}$ converges or not

Evaluate $\lim_{(x,y,z)\to (0,0,0)}\frac{1}{x^2+y^2+z^2}e^{-\frac{1}{\sqrt{x^2+y^2+z^2}}}$

Given any non-real, complex number with positive real part, must some power of it has negative real part?

For what $\alpha$ and $\beta$ values does $\lim_{(x,y)\to (0,0)}$ $\frac {| x|^{\alpha}| y|^{\beta}}{\ x^4 + y^4 }$ goes to $0$?

Integrate indefinite integral

Evaluate $\lim_{h\to 0}\frac{1}{h^3e^{\frac{1}{\sqrt{h^2}}}}$

Continuity and close map . [Metric Space.]

Proving uniform continuity of the exponential function on a semi-finite interval

Prove that a metric space $S$ is disconnected iff $\exists$ a non empty subset $A$ of $S$ s.t. $A \neq S$ and $A$ is both open and closed.

Are points negligible for weak derivative in dimension 2?

Proving that the counting measure is a measure on $\mathcal A$

Metric Space (Continuity)

How to prove that $L^{\infty}([0,1]) \subset L^q([0,1]) \subset L^p([0,1])$?

Pointwise a.e. convergence vs. Pointwise convergence

Prove that $f(x,y) = \sqrt{x^2 + y^2}$ is continuous at $a=(3,\frac{1}{2})$

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