Eelvex
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870
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 13 Infinitely many integer solutions for the equations $x^3+y^3+z^3=1$ and $x^3+y^3+z^3=2$ 8 Show $\lim_{n\to \infty}n\int_{0}^{\frac{\pi}{2}}(1-\sqrt[n]{\sin(x)})\,\mathrm{d}x = \frac{\pi \ln(2)}{2}$ 6 Intuitive Understanding of the constant “e” 4 Dividing by 1000 twice? 4 Prove $\sin(\pi/2)=1$ using Taylor series

### Reputation (870)

 +5 Function that maximizes a function +10 evaluating compositions of trigonometric functions that do not use standard points or angles from the unit circle +10 Show $\lim_{n\to \infty}n\int_{0}^{\frac{\pi}{2}}(1-\sqrt[n]{\sin(x)})\,\mathrm{d}x = \frac{\pi \ln(2)}{2}$ +10 How to prove $\lim_{n \to \infty} e^n \cdot \left( \sum_{k=0}^{n-1} ({k-n \over e})^k/k! \right)- 2 \cdot n = \frac 23$?

### Questions (9)

 18 Number of moves to solve a flood-it/sock-dye game 5 Function that maximizes a function 3 How to calculate circumference of circle in $L^p$? 3 Is there a name for this bipartite graph problem? 3 Finding probability of an unfair coin

### Tags (32)

 16 elementary-number-theory × 2 6 calculus × 6 13 diophantine-equations 6 intuition 13 number-theory 5 real-analysis × 2 8 integration 5 sequences-and-series × 2 7 puzzle × 2 4 inequality

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