Activity for Anonymousâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #286682 |
Post edited: |
— | over 2 years ago |
| Edit | Post #286682 | Initial revision | — | over 2 years ago |
| Answer | — |
A: equilateral triangle inscribed in an ellipse We will show that there can be at most three equilateral triangles inscribed in the ellipse passing through $(0,-2)$, so you must already have all the solutions. Let $A = (0,-2)$ and let $E$ be the ellipse $x^2 + 3y^2 = 12$. We have $A \in E$. Now let us search for equilateral triangles $ABC$ i... (more) |
— | over 2 years ago |
| Edit | Post #286451 | Initial revision | — | over 2 years ago |
| Answer | — |
A: $g(x)\xrightarrow{x\to\infty}\infty$ Implies $g'(x)\leq g^{1+\varepsilon}(x)$ We may restrict attention to an interval $I = (A,+\infty)$ on which $g(x) > 1$. Let $\varepsilon > 0$ be given. The set $S$ of points $x$ in $I$ at which $g'(x) > (g(x))^{1 + \varepsilon}$ is open, hence is a disjoint union of countably many open intervals of the form $(a,b)$. Given such an int... (more) |
— | over 2 years ago |