List questions from real-analysis

Published on 12 Apr 2026 - 2:55

125

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Computing $\lim\limits_{x\to0}\int_0^x\frac{t^2}{(x-\sin x)\sqrt{a+t}}\,dt$ without L'Hopital

Published on 15 Apr 2026 - 10:15

97

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what is the largest open set contained in {${x|f(x)=g(x)} $}?

Published on 12 Apr 2026 - 16:05

360

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Non measurable function verification

Published on 11 Apr 2026 - 15:27

74

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Let $\ell =\lim\limits_{x\to b}\frac{f(x)-cb}{g(x)-b^2}$then compute $c-\ell $.

Published on 14 Apr 2026 - 16:31

719

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Is the inverse of bijective continuous functions always continuous?

Published on 10 Apr 2026 - 23:14

247

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Prove the convergence of $\sum\limits_{k=2}^\infty \frac 1 {(2k+1)(2k+5)}$

Published on 15 Apr 2026 - 4:47

577

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Arzelá-Ascoli Theorem precompact sets

Published on 15 Apr 2026 - 9:32

80

Views

proving existence of a particular linear operator on the space of bounded functions

Published on 09 Apr 2026 - 5:33

312

Views

Smooth functions of compact support and continuous functions on the closure

Published on 11 Apr 2026 - 14:51

35

Views

Uniform Convergence of $(f_{n}^2)_{n}$

Published on 14 Apr 2026 - 17:41

211

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Find $\lim_{n\rightarrow\infty} \frac{\log(2 + 3^{n})}{2n}$

Published on 29 Mar 2026 - 11:13

245

Views

Isometry maps closed unit ball to closed unit balI

Published on 13 Apr 2026 - 6:04

108

Views

How to solve $\lim\limits_{x\to 3}\frac{1}{(9-x^2)^2}\left( \frac{9+x^2}{3x}-2\sin \frac{3π}{2}\sin\frac{πx}{2}\right)$ Without L'Hopital.

Published on 24 Mar 2026 - 22:01

114

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Arcwise connected sets

Published on 12 Apr 2026 - 0:48

List Question

Assumption of proof with contrapositive

Computing $\lim\limits_{x\to0}\int_0^x\frac{t^2}{(x-\sin x)\sqrt{a+t}}\,dt$ without L'Hopital

what is the largest open set contained in {${x|f(x)=g(x)} $}?

Non measurable function verification

Let $\ell =\lim\limits_{x\to b}\frac{f(x)-cb}{g(x)-b^2}$then compute $c-\ell $.

Is the inverse of bijective continuous functions always continuous?

Prove the convergence of $\sum\limits_{k=2}^\infty \frac 1 {(2k+1)(2k+5)}$

Arzelá-Ascoli Theorem precompact sets

proving existence of a particular linear operator on the space of bounded functions

Smooth functions of compact support and continuous functions on the closure

Uniform Convergence of $(f_{n}^2)_{n}$

Find $\lim_{n\rightarrow\infty} \frac{\log(2 + 3^{n})}{2n}$

Isometry maps closed unit ball to closed unit balI

How to solve $\lim\limits_{x\to 3}\frac{1}{(9-x^2)^2}\left( \frac{9+x^2}{3x}-2\sin \frac{3π}{2}\sin\frac{πx}{2}\right)$ Without L'Hopital.

Arcwise connected sets

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