## Analysis

### Important threads

### Threads

- Calculus of Variations, Euler-Lagrange Equation and Brachistochrone Problem. (1 Reply)
- Prove that $f_n(x)\rightrightarrows 0$ in $[0,+\infty)$, where $f_n(x)=\frac{x-x^2}{1+x^n}$ (0 Replies)
- Find all $\alpha\in\mathbb{R}$ such that $\forall n\,\exists m\;|\alpha-m/n| < 1/(3n)$ (0 Replies)
- Spivak Calculus on Manifolds Exercises (0 Replies)
- Complex Numbers (1 Reply)
- Notes from [Kevin O'Neill: An Introduction to Non-Standard Analysis and its Applications] (1 Reply)
- A tricky integral (2 Replies)
- Regular polygon approximation of $\pi$ (0 Replies)
- An interesting bijection $\varphi: \mathbb{N}^+ \to \mathbb{Q}^+$ (4 Replies)
- Evaluate \(\int_0^{\infty}\left(\ln (x^2+1)/(x^2+1) \right)dx\) (2 Replies)
- Limits of sequences (9 Replies)
- Determine the convergence of series (3 Replies)
- Convergence of a series (2 Replies)
- Limit of a recursion sequence (0 Replies)
- Taylor's Theorem (Taylor polynomial) (0 Replies)
- Function limits (1 Reply)
- The harmonic sequence (1 Reply)
- Tough Infinite series (0 Replies)
- Improper Integral (1 Reply)
- Evaluate Series (1 Reply)