New posts in real-analysis

Integral of $d$ dimension Calculation

real-analysis integration complex-analysis analysis improper-integrals

$f$ continuous on $(a,b)$ and $|f|$ differentiable on $(a,b)$; is $f$ differentiable in $(a,b)$?

real-analysis derivatives continuity

Open set containing rationals but complement non-denumerable

real-analysis general-topology examples-counterexamples

A converse proposition to the Mean Value Theorem [duplicate]

real-analysis derivatives

Two definitions for derivative

real-analysis limits derivatives definition

How to prove that $\lim_{k\to+\infty}\frac{\sin(kx)}{\pi x}=\delta(x)$?

real-analysis calculus distribution-theory dirac-delta

Convergence of $\sum_{n=0}^{\infty}\sin(x\pi n!)$

real-analysis sequences-and-series diophantine-approximation

Composition of a continuous function and a discontinuous function, can be continous.

If a series $\sum\limits_{k=1}^{\infty}a_{k}$ converges, then $(a_{k})\to 0$.

real-analysis sequences-and-series

Identify the boundary of $\mathbb{Q}$ in the discrete metric space $\mathbb{R}$

real-analysis metric-spaces

Positivity of the weak * limit in $L^{\infty}$. [closed]

real-analysis weak-convergence

Uniform convergence when $a \lt b$ but not if $a \geq b$

real-analysis convergence-divergence uniform-convergence supremum-and-infimum pointwise-convergence

Limits of $ f(x,y) = y\ (1-x)^{y-2} $ reach contradiction

real-analysis limits multivariable-calculus solution-verification fake-proofs

Finding Taylor's series of the function: $\frac{e^{a \sin^{-1}x}}{\sqrt{1-x^2}}$

real-analysis sequences-and-series power-series taylor-expansion

Convergence in $L_{\infty}$ norm implies uniform convergence

real-analysis measure-theory

Change of order of double limit of function sequence

real-analysis sequences-and-series functions limits

An outer measure is countable-additive on the measurable sets

real-analysis measure-theory lebesgue-measure

$f$ is continuous on $X$ iff $f$ is continuous on every compact subset

real-analysis proof-verification

Closed form of $x_{n+1} =\frac{1}{2}\left(x_n-\frac{1}{x_n}\right)$ with $x_0 \neq 0,1$

calculus real-analysis sequences-and-series algebra-precalculus closed-form

Finding the maximum and minimum values of $f(x)=a^x+a^{1/x}$

real-analysis functions