List questions from analysis

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Does this set have a maximum?

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Proof; Log Convex implies Convexity

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Characterization of vectors such that a linear transformation has the property $\|Mx\| > \rho(M)\|x\|$

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$\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?

Published on 30 Mar 2026 - 0:00

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Prove that a function have no maximum

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Understanding the essential range

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Example of differential equation

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How to prove $\lim_{h \to 0} θ ＝ \frac{1}{n＋1} $?

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Differentiability of the function:$g(x,y)=f(\sqrt{x^2+y^2})$

Published on 21 Mar 2026 - 17:53

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Finding: $\lim\limits_{m\to\infty}\left(\sqrt[m]{m+1}\cdot\sqrt[m^2+m]{\binom{m}{1}\binom{m}{2}\cdots\binom{m}{m}}\right) .$

Published on 12 Mar 2026 - 12:48

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Injectivity of a function $\frac{x}{1+|x|}$

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Proving that $b-a\ge \pi $

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Identifying $C(X\times X)$ with $C(X)\otimes C(X)$

Published on 03 Apr 2026 - 15:38

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If $A\subseteq(0,+\infty)$ is nonempty and closed under addition then it is not bounded above.

Published on 03 Apr 2026 - 9:51

List Question

Prove $f(x,y)$ is continuous or not continuous.

Does this set have a maximum?

Proof; Log Convex implies Convexity

Characterization of vectors such that a linear transformation has the property $\|Mx\| > \rho(M)\|x\|$

$\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?

Prove that a function have no maximum

Understanding the essential range

Example of differential equation

How to prove $\lim_{h \to 0} θ ＝ \frac{1}{n＋1} $?

Differentiability of the function:$g(x,y)=f(\sqrt{x^2+y^2})$

Finding: $\lim\limits_{m\to\infty}\left(\sqrt[m]{m+1}\cdot\sqrt[m^2+m]{\binom{m}{1}\binom{m}{2}\cdots\binom{m}{m}}\right) .$

Injectivity of a function $\frac{x}{1+|x|}$

Proving that $b-a\ge \pi $

Identifying $C(X\times X)$ with $C(X)\otimes C(X)$

If $A\subseteq(0,+\infty)$ is nonempty and closed under addition then it is not bounded above.

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