New posts in real-analysis

Why is it true that every finite-dimensional inner product space is a Hilbert space?

A triangle has one vertex at a circle's center and two vertices on the circle. Can the three enclosed regions have rational areas?

real-analysis geometry number-theory trigonometry

limit infimum and limit of a sequence of functions

real-analysis limits supremum-and-infimum

Show that $f'(x) = \lim\limits_{h \rightarrow 0} \dfrac{f(x+h)-f(x-h)}{2h}$

calculus real-analysis limits derivatives

Is there a counter example for this statement?

real-analysis examples-counterexamples uniform-continuity

Evaluating $ \sum\limits_{n=1}^\infty \frac{1}{n^2 2^n} $

calculus real-analysis sequences-and-series algebra-precalculus summation

Weaker Condition than Differentiability that Implies Continuity

real-analysis continuity

Solving $x^x=\frac{1}{\sqrt 2}$

For $\sum_{n=1}^\infty z^n \frac{P(n)}{Q(n)}$ where $Q(n)$ and $P(n)$ are polynomials, does di(con)vergence only depends on $z$?

real-analysis sequences-and-series

Work out a function formula from existing points

real-analysis calculus

Monotonicity of $\ell_p$ norm

real-analysis functional-analysis optimization normed-spaces lp-spaces

Is the infinite-dimensional unit sphere compact?

real-analysis analysis functional-analysis

Is there a way to prove this exponential inequality: if $a>b$ then $a^a>b^b$ for $a,b>1$?

real-analysis algebra-precalculus functions inequality exponential-function

Does this derivation on differentiating the Euclidean norm make sense?

Can a function have a derivative where it has no value?

calculus real-analysis

Compare $\arcsin (1)$ and $\tan (1)$

real-analysis trigonometry inequality inverse-function number-comparison

Confusion in fundamental theorem of calculus

calculus real-analysis integration

If $f(x) = h(x)g(x)$, is $h$ differentiable if $f$ and $g$ are?

What is the easy way to calculate the roots of $z^4+4z^3+6z^2+4z$?

calculus real-analysis complex-analysis self-learning

How to prove a polynomial can be written as Taylor-style?

calculus real-analysis derivatives power-series taylor-expansion