New posts in real-analysis

Limit of maximum of $f_{n}(x)=\frac{1}{n}(\sin{x}+\sin{(2x)}+\cdots+\sin{(nx)})$

real-analysis sequences-and-series limits fourier-analysis trigonometric-series

Uniform Convergence verification for Sequence of functions - NBHM

real-analysis proof-verification uniform-convergence alternative-proof

$g(x)$ is continuous on $\mathbb{R}$ st $g(x)=g(x^2)$. Prove that $g(x)$ is constant.

real-analysis continuity

Real Analysis : Self Studying vs Doing a Course

real-analysis analysis self-learning

A continuous function that maps closed unit square to the unit open square

real-analysis general-topology continuity metric-spaces solution-verification

$a_1=\sqrt{6}$ , $a_{n+1} = \sqrt{6+a_n}$

real-analysis sequences-and-series

Determine the extrema of $\int^{x^2}_1\frac{\sin t}{2+e^t}\,dt$

A question about the vector space spanned by shifts of a given function

real-analysis linear-algebra functional-analysis derivatives

Taylor series not converging, other example than $\exp(-1/x^2)$?

calculus real-analysis convergence-divergence taylor-expansion

Could Euclid have proven that real number multiplication is commutative?

real-analysis geometry euclidean-geometry math-history real-numbers

Product of metric outer measures

real-analysis measure-theory set-theory

$\sum \frac{a_n}{\ln a_n}$ converges $\implies \sum \frac{a_n}{\ln (1+n)}$ converges

real-analysis sequences-and-series

Can we find a function $f:\mathbb{R}\rightarrow \mathbb{R}$ that is open, closed, but not continuous?

calculus real-analysis reference-request

Connection between finiteness of dimension of a vector space and existence of a polynomial, such that P(T) is a zero map.

limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$

calculus real-analysis sequences-and-series convergence-divergence recurrence-relations

Uniform convergence problem

real-analysis sequences-and-series convergence-divergence

Find the max and min values for $f(x,y)=y^2-x^2$ subject to $(1/4)x^2+y^2=1$ using the Lagrange Multiplier

real-analysis multivariable-calculus maxima-minima lagrange-multiplier

Calculating limit using sub sequences $\lim\limits_{n\to\infty }\frac{(-5)^{n}+2\cdot(-2)^{n}+3}{5^{n+1}+2\cdot(-3)^{n}+3}$

Show that Series $\sum \frac{2^{n}(z+3)^{n}}{3n}$

real-analysis complex-analysis

Application of the Arzela-Ascoli Theorem

real-analysis functional-analysis functions partial-differential-equations weak-convergence