Young
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### Questions (116)

 30 How to show that $f'(x)<2f(x)$ 19 Finding $\prod_{n=1}^{999}\sin\left(\frac{n \pi}{1999}\right)$ 11 How do I solve this exponential equation? $5^{x}-4^{x}=3^{x}-2^{x}$ 11 How to prove that $\frac{d^n}{dx^n}(x^2-1)^n=0$ has $n$ real roots? 8 sum and product of two rational numbers are both integers

### Reputation (1,906)

 +28 Find $f(x)$ given that: $f'(x)=\frac{f(x)-x}{f(x)+x}$ +28 Find that $\lim_{a\to \infty}a^3 f(a)=?$ +35 $f \colon \mathbb{R} \rightarrow \mathbb{R}$, $f$ is continuous , and $f(x+1)+f(x)=x^2$ +5 Finding minimum $\frac{x+y}{z}+\frac{x+z}{y}+\frac{y+z}{x}$

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### Tags (48)

 0 calculus × 15 0 integration × 7 0 real-analysis × 15 0 limits × 6 0 sequences-and-series × 12 0 functional-equations × 6 0 combinatorics × 10 0 elementary-number-theory × 6 0 inequality × 9 0 combinatorial-proofs × 5

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