Tag: calculus
- $(a_n) \in \ell^1 \implies (a_n n \log(n)) \in \ell^\infty$
- Solve: If $x+y=8$, what is the max of $x^y$
- A troubling differential equation: $(xy+2y+x+2)y’=e^{-y}(x+3)$
- The relevance of “for all $x$” in this epsilon-delta definition, rather than just having a single $x$
- How should I find the function $y(x)$ by using the method of Lagrange multipliers
- Infinitesimal step in different coordinates
- Show that $\sum_{n=1}^{\infty} \frac{\binom{2n}{n} (H_{2n} – H_n)}{4^n (2n – 1)^2} = 2 + \frac{3\pi}{2} \log(2) – 2G – \pi$
- Show that $\int_0^{\pi/3}\arccos(2\sin^2 x-\cos x)\mathrm dx=\frac{\pi^2}{5}$
- Integral $I = \int_0^1 \frac{\sqrt{x^3 + 1}}{(x^5 + x^2 + 1)} \ln\left(\frac{x^6 + x^3 + 1}{x^6 – x^3 + 1}\right) \, dx.$
- Integrating over unit sphere, using Haar measure