New posts in real-analysis

Let $(f(x))^2$ and $(f(x))^3$ are $C^{\infty}$. Prove or disprove that $f$ is $C^{\infty}$.

real-analysis functions

For which real numbers $c$ is $\frac{e^x+e^{-x}}{2} \le e^{cx^2}$ for all real numbers $x$?

calculus real-analysis

Is the interval for the middle point of the Mean Value Theorem open or closed?

Is the set $S=\{(x,y)\in\Bbb R^2\mid e^{x^2+y^2}=2+x^2+y^2\}$ bounded?

real-analysis multivariable-calculus solution-verification

The limit of $f'(x)=b$ implies that $f$ is differentiable at that point [duplicate]

Dimension for a closed subspace of $C[0,1]$.

real-analysis functional-analysis banach-spaces

Is the space $B([a,b])$ separable?

real-analysis general-topology analysis functional-analysis metric-spaces

Prove that $\sum_{k=2}^{\infty} \frac{k^s}{k^{2s}-1}> \frac{3\sqrt{3}}{2}(\zeta(2s)-1),\space s>1$

calculus real-analysis sequences-and-series inequality

what is the difference between a set's closure and completion?

real-analysis general-topology

Function $f$ with $|f|$ is Lebesgue integrable but $f$ isn't locally Lebesgue integrable

real-analysis integration analysis lebesgue-integral

Limit without hospital's rule $\lim_{x\rightarrow 0} (\frac{1}{x^2} - \frac{x}{\sin^3(x)})$

real-analysis limits limits-without-lhopital

To what function does this series converge?

calculus real-analysis sequences-and-series functions convergence-divergence

Two powerful alternating sums $\sum_{n=1}^\infty\frac{(-1)^nH_nH_n^{(2)}}{n^2}$ and $\sum_{n=1}^\infty\frac{(-1)^nH_n^3}{n^2}$

real-analysis integration sequences-and-series harmonic-numbers polylogarithm

Number of zeros of $f(x)= \frac{1}{2} E\left[ \tanh \left( \frac{x+Z}{2} \right) \right]-\tanh(x)+\frac{x}{2}$ where $Z$ is standard normal

real-analysis probability roots hyperbolic-functions

Set of Finite Measure: Uncountable disjoint subsets of non-zero measure

Why does the sup norm make the results of approximation theory independent from the unknown distribution of the input data?

real-analysis functional-analysis machine-learning approximation-theory neural-networks

Equivalent definition for an open interval around a point in $\mathbb{R}$

real-analysis real-numbers interval-arithmetic

Does $f_{n}(x)=n\cos^n x \sin x$ uniformly converge for $x \in [0,\frac{\pi}{2}]$?

calculus real-analysis convergence-divergence

Chain rule for Hessian matrix

real-analysis analysis multivariable-calculus vector-analysis

Extending continuous and uniformly continuous functions

real-analysis continuity