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 10 When evaluating a limit by making a change of variable, how does the sign (+/-) change? 7 How to intuitively think of this definition 7 Evaluate an infinite product in a closed form $\prod\limits_{n=1}^{\infty} \frac{1}{1+\pi^{1/{2^n}}}$ 7 The mean of the of a sum is the sum of the means 6 Is there a formal way to show that $X \cap Y \subseteq X$.

### Reputation (4,668)

 +10 The mean of the of a sum is the sum of the means +10 Prove or disprove that integral term is log-concave +10 Integration constants +10 what is the Nash equilibrium in a Third price auction?

### Questions (2)

 8 Is it true that $\phi(\mu)=\mu F(\mu)^2-\int_{\mu}^{\overline{v}}F(v)[1-F(v)]dv\geq 0$? 2 Prove $f(x^D)\geq1$: $f$ is a log-concave density and $\frac{1-2F(x^D)}{f(x^D)}=x^D-\frac{1}{2}$

### Tags (142)

 38 calculus × 43 19 multivariable-calculus × 15 27 real-analysis × 15 18 functions × 16 23 limits × 4 18 linear-algebra × 14 22 probability × 17 14 elementary-set-theory × 6 19 derivatives × 18 11 partial-derivative × 15

### Bookmarks (5)

 29 Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$ 22 Find all functions that satisfy $f(\frac{x+4}{1-x}) + f(x) = x$ 10 If $\int_0^x f^2(t)dt \le f(x)$ for all $x \in [0,1]$, then $\min_{[0,1]} f(x) \le 1$? 8 Prove that $f$ is additive if $f(x)f(x-y)+f(y)f(x+y)= f(x)^2+f(y)^2$ 4 How to solve the equation $xy = 1, x^{2x-y} = y^{2(x-y)}$

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