New posts in real-analysis

Finding the sum of the series $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$

real-analysis sequences-and-series

Evaluate $\lim_{x\to 0}\frac{e^{(x+1)^{1/x}}-(x+1)^{e/x}}{x^2}$

real-analysis limits

Show that $(f_n)$ is equicontinuous, given uniform convergence

real-analysis sequences-and-series

Justification of substitution in finding indefinite integrals

calculus real-analysis integration indefinite-integrals

Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $

real-analysis inequality integration

Fubini's theorem for Riemann integrals?

Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$

real-analysis analysis asymptotics

equivalency of weak and strong convergence

real-analysis functional-analysis

Changing the values of an integrable function $f:[a,b] \to \mathbb R$ countably infinitely many points not a dense subset of $[a,b]$

real-analysis integration analysis

Find the gradient and hessian of $f(Ax+b)$ for real value $f$ and matrix $A$

calculus real-analysis multivariable-calculus derivatives

Function $f$ s.t. $\lim_{x\to\infty}\frac{f(e^x)}{f(x)}=1$

real-analysis sequences-and-series limits divergent-series tetration

For what $a\neq0$ does $a_{n+1}=1/a_{n}+a_{n}/2$ the sequence converge

real-analysis fixed-point-theorems

A simpler proof of Jensen's inequality

real-analysis measure-theory inequality

Show $f(x) = x^3 - \sin^2{x} \tan{x} < 0$ on $(0, \frac{\pi}{2})$

calculus real-analysis trigonometry

Total variation metric space and its equivalence classes

real-analysis metric-spaces

f(x,y) not Differentiable on (0,0)

real-analysis limits analysis derivatives continuity

continuous onto function from irrationals in [0,1] onto rationals in [0,1]

Can subsequences be finite?

Real Analysis - Convergence [closed]

real-analysis sequences-and-series convergence-divergence

Can I split this into two series and apply the alternating series test?

real-analysis sequences-and-series