Newbetuts

A is a subset of a metric space under given conditions. Prove there is a $y \in A$ that minimizes the distance from $x$ to elements of $A$

Maclaurin expansion of $\arctan(x)/(1 − x).$

$\int_a^bf^2(x)\,dx\le \frac{2}{3}\int_a^bf(x)\,dx$ for a convex differentiable function

Is a germ equivalent to an infinite jet?

Prove that $e$ is transcendental.

Regarding evaluation of the limit of the sequence $\Bigl(\frac{1}{n}\Bigr)^n+\Bigl(\frac{2}{n}\Bigr)^n+ \cdots \Bigl(\frac{n}{n}\Bigr)^n$ [duplicate]

Family of Generalized Integrals ${I}(a,b,p)=\int_0^{ab} \left( \left\{\frac{x}{a}\right\}-p\right) \left( \left\{\frac{x}{b}\right\}-p\right) \; dx$

Prove two series are equal

Proof of Clairaut’s theorem in Terence Tao Analysis 2

The domino curve

Proving function is $C^k$

De-mystifying tricks in proof – If $\{x_n\}$ converges, then Cesaro Mean converges.

Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$

Two proper subsets of the real numbers, $A$ and $B$, that have the following conditions: $A$ and $B$ are closed, $A \cap B$ is empty, +1

Conditional expectation of pullback of sigma algebra

Sequence of function depending on $n$ and $\epsilon$

New posts in real-analysis

Rigorous, real analysis, proof of De Moivre–Laplace theorem

Moments and weak convergence of probability measures

Is there a symbol for a number exactly greater than another [closed]

Ask about the extreme value theorem. [closed]

A is a subset of a metric space under given conditions. Prove there is a $y \in A$ that minimizes the distance from $x$ to elements of $A$

Maclaurin expansion of $\arctan(x)/(1 − x).$

$\int_a^bf^2(x)\,dx\le \frac{2}{3}\int_a^bf(x)\,dx$ for a convex differentiable function

Is a germ equivalent to an infinite jet?

Prove that $e$ is transcendental.

Regarding evaluation of the limit of the sequence $\Bigl(\frac{1}{n}\Bigr)^n+\Bigl(\frac{2}{n}\Bigr)^n+ \cdots \Bigl(\frac{n}{n}\Bigr)^n$ [duplicate]

Family of Generalized Integrals ${I}(a,b,p)=\int_0^{ab} \left( \left\{\frac{x}{a}\right\}-p\right) \left( \left\{\frac{x}{b}\right\}-p\right) \; dx$

Prove two series are equal

Proof of Clairaut’s theorem in Terence Tao Analysis 2

The domino curve

Proving function is $C^k$

De-mystifying tricks in proof – If $\{x_n\}$ converges, then Cesaro Mean converges.

Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$

Two proper subsets of the real numbers, $A$ and $B$, that have the following conditions: $A$ and $B$ are closed, $A \cap B$ is empty, +1

Conditional expectation of pullback of sigma algebra

Sequence of function depending on $n$ and $\epsilon$