Intereting Posts

Functional equation $f(xy)=f(x)+f(y)$ and differentiability
Importance of a result in measure theory
Taking a derivative with respect to a matrix
Summing over General Functions of Primes and an Application to Prime $\zeta$ Function
Most ambiguous and inconsistent phrases and notations in maths
Characteristic polynomial of $T:M_n(\mathbb{F}) \rightarrow M_n(\mathbb{F}) ,\ \ TX = AX \ \ (A\in M_n(\mathbb{F}))$
Prove that a function is constant
Second Fundamental Form of Hypersurface
Proof that determinant rank equals row/column rank
Quadratic reciprocity via generalized Fibonacci numbers?
Defining the Lie Bracket on $\mathfrak{g} \otimes_\Bbb{R} \Bbb{C}$
Relation between exclusive-OR and modular addition in a specific function
Statistical Inference Question
Maximal real subfield of $\mathbb{Q}(\zeta )$
Optimal multiplying method

$$\lim_{x \to \frac{2}{\pi}}\lfloor \sin \frac{1}{x} \rfloor=0$$

I need to prove the limit of this using the $\epsilon – \delta $ way but I don’t know how to find $\delta$ when I’m given a trigonometric function I know only how to do it with polynomial functions

- Integration of exponential and square root function
- Some integral with sine
- log sin and log cos integral, maybe relate to fourier series
- Is $\sin(x)/ \tan(x) = \cos(x)$ at $0$?
- Is there a tangent of $x\sin(1/x)$ at $x = 0$?
- What did Newton and Leibniz actually discover?

- Show $g(x)=\frac{x \sin x}{x+1}$ has no maxima in $(0,\infty)$
- Show that it is possible that the limit $\displaystyle{\lim_{x \rightarrow +\infty} f'(x)} $ does not exist.
- Not sure about the derivative of the integral
- Optimisation Problem on Cone
- Uniform convergence of $\sum_{n=0}^{\infty} \frac{\int_{\sin nx}^{\sin(n+1)x}\sin t^2dt \int_{nx}^{\infty}\frac{dt}{\sqrt{t^4+1}}}{1+n^3x^2}$
- Proving that a definition of e is unique
- Closed form for $\sum_{n=0}^\infty\frac{\operatorname{Li}_{1/2}\left(-2^{-2^{-n}}\right)}{\sqrt{2^n}}$
- prove the divergence of cauchy product of convergent series $a_{n}:=b_{n}:=\dfrac{(-1)^n}{\sqrt{n+1}}$
- Issue with Spivak's Solution
- Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f'(x)$ is continuous and $|f'(x)|\le|f(x)|$ for all $x\in\mathbb{R}$

- How to divide aleph numbers
- Proof of the polynomial division algorithm
- When does the set enter set theory?
- What can we actually do with congruence relations, specifically?
- Intuition behind variational principle
- Solution for exponential function's functional equation by using a definition of derivative
- Integrability: Neither improper Riemann nor Lebesgue but Henstock-Kurzweil
- Simultaneous diagonalization of quadratic forms
- A morphism of free modules that is an isomorphism upon dualization.
- Proof of no prime-representing polynomial in 2 variables
- Working with Equivalence Classes and Quotient Sets
- Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
- Solving a Diophantine equation of the form $x^2 = ay^2 + byz + cz^2$ with the constants $a, b, c$ given and $x,y,z$ positive integers
- Odds of winning at minesweeper with perfect play
- Evaluating $\sum_{n=1}^\infty \frac{n^2}{3^n} $