# chloe_shi

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# 47 Questions

 14 Solving Differential Functional Equation $f(2x)=2f(x)f'(x)$ 8 Range Of $\frac{|a+b|}{|a|+|b|}+\frac{|b+c|}{|b|+|c|}+\frac{|c+a|}{|c|+|a|}$ 7 Number of real roots of $\sum_{k=0}^{n}\frac{x^{k}}{k!}=0$ 6 Inequality Of Four Variables 5 $1^{k}+2^{k}+\cdots+n^{k}$ is not divisible by $n+2$

# 1,625 Reputation

 +5 Geometric Inequality Related To Median, Altitude +10 Algebraic inequality:$\frac a{b^2} + \frac b{c^2} +\frac c{a^2} \geq \frac1a+\frac1b+ \frac1c$ +5 Equal Angle Related To Midpoints In Quadrilateral +10 Proof on an equilateral triangle with a cevian extended to its circumcircle

 7 How many digits does the number $200^{2010}$ have? 6 If $\lim\limits_{x\to\infty} xf(x) = L$, then $\lim\limits_{x\to\infty} f(x) =0$ 5 Algebraic inequality:$\frac a{b^2} + \frac b{c^2} +\frac c{a^2} \geq \frac1a+\frac1b+ \frac1c$ 5 In a triangle $\angle A = 2\angle B$ iff $a^2 = b(b+c)$ 4 Find length of $CD$ where $\angle BCA=120^\circ$ and $CD$ is the bisector of $\angle BCA$ meeting $AB$ at $D$

# 28 Tags

 50 geometry × 29 11 contest-math × 4 17 trigonometry × 8 9 analysis × 3 13 circle × 5 8 calculus × 4 12 inequality × 22 7 sequences-and-series × 10 11 limits × 6 7 triangle × 4

# 1 Account

 Mathematics 1,625 rep 312