List questions from real-analysis

Published on 08 Apr 2026 - 21:09

44

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To show that $\bigcup_{n\in \mathbb{N}}[-n,n]=\mathbb{R}$

Published on 25 Jan 2018 - 12:50

57

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Find the Supremum of $B$

Published on 12 Apr 2026 - 19:26

172

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Derivative of $\tan x$ without using derivative of $\sin x$ and $\cos x$

Published on 31 Mar 2026 - 13:36

103

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How to prove that $\sum _{p}\sum_{k = 2}^\infty \frac{1}{kp^k}$ is convergent?

Published on 12 Apr 2026 - 0:30

58

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Find the limit of $c_n$.

Published on 12 Apr 2026 - 16:57

36

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Is a compact set with respect to the product topology measurable?

Published on 10 Apr 2026 - 18:12

185

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Bounding the power of a sum

Published on 12 Apr 2026 - 14:26

96

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Let $f\left(x\right)=\begin{cases} 0 & -1\leq x\leq0\\ x^4 & 0<x\leq1 \end{cases}$. In the taylor's formula for x=0 with maximum possible value of n

Published on 25 Mar 2026 - 1:18

1.5k

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Find the largest term of the sequence $a_n=\sqrt[n]{n}$

Published on 24 Mar 2026 - 23:45

126

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$\sum a_nb_n$ convergence theorem (Rudin)

Published on 09 Apr 2026 - 2:23

41

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Finding a constant that does not depend on a parameter

Published on 25 Mar 2026 - 7:47

79

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Limit of $x^2(1 - x \sin \frac{1}{x})$ as $x \to \infty$

Published on 26 Mar 2026 - 10:48

28

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Why $\Phi_X(\partial P_{N,p})+\Phi_X(\partial P_{N,q})=\Phi_X(P_{N,p}\cup P_{N,q})$?

Published on 31 Mar 2026 - 23:28

167

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Another solution.

Published on 09 Apr 2026 - 22:36

List Question

Proving that the sequence $\{\frac{3n+5}{2n+6}\}$ is Cauchy.

To show that $\bigcup_{n\in \mathbb{N}}[-n,n]=\mathbb{R}$

Find the Supremum of $B$

Derivative of $\tan x$ without using derivative of $\sin x$ and $\cos x$

How to prove that $\sum _{p}\sum_{k = 2}^\infty \frac{1}{kp^k}$ is convergent?

Find the limit of $c_n$.

Is a compact set with respect to the product topology measurable?

Bounding the power of a sum

Let $f\left(x\right)=\begin{cases} 0 & -1\leq x\leq0\\ x^4 & 0<x\leq1 \end{cases}$. In the taylor's formula for x=0 with maximum possible value of n

Find the largest term of the sequence $a_n=\sqrt[n]{n}$

$\sum a_nb_n$ convergence theorem (Rudin)

Finding a constant that does not depend on a parameter

Limit of $x^2(1 - x \sin \frac{1}{x})$ as $x \to \infty$

Why $\Phi_X(\partial P_{N,p})+\Phi_X(\partial P_{N,q})=\Phi_X(P_{N,p}\cup P_{N,q})$?

Another solution.

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