Educ

### Questions (270)

 12 Solve $\lim_{x\to +\infty}\frac{x^x}{(\lfloor x \rfloor)^{\lfloor x \rfloor }}$ 9 $7\mid x \text{ and } 7\mid y \Longleftrightarrow 7\mid x^2+y^2$ 9 Change of variables for stochastic integral 8 $\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits. 7 Does $\sum_{n\geq 2} \frac{\ln(1+n)}{\ln(n)}-1$ converge/diverge?

### Reputation (2,347)

 +5 Show that $dX_t=1_{X_t\not=0} dW_t$ does not have a pathwise unique solution. +10 If $g\circ f$ is injective and $f$ is surjective then $g$ is injective +5 Taylor expansion of $\frac{(-1)^n}{\ln n(1+\frac{1}{n\ln n}+o(\frac{1}{n\ln n})}$ +5 Crossed Ladders Problem

 1 If $g\circ f$ is injective and $f$ is surjective then $g$ is injective 1 Two apparently different evaluations of $\int \frac{x-1}{9x^2-18x+17}dx$ 1 prove $e^{bt} \ \int_0^t \ f(s) ds=\int_0^t \ ( e^{-bs} \ f(s)-be^{-bs}\int_0^s\ f(u)\ du) \ ds$ 0 Computing $\int (1 - \frac{3}{x^4})\exp(-\frac{x^{2}}{2}) dx$ 0 Solving Equation $x^2-(2+i)x+(-1+7i)=0$

### Tags (131)

 2 integration × 25 0 real-analysis × 95 1 functions × 10 0 sequences-and-series × 42 1 lebesgue-integral × 4 0 analysis × 39 1 indefinite-integrals × 2 0 taylor-expansion × 32 0 calculus × 120 0 asymptotics × 27