pxchg1200

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bio website pxchg1200.is-programmer.com location China age 22 member for 1 year, 9 months seen 12 hours ago profile views 515

I love mathematics very much! especially analysis,and inequality.Here is my blog,Welcome to visit. :D

21 Questions

 15 Prove $f(x)=ax+b$ 12 Show $\varlimsup_{n\rightarrow\infty}{\sqrt[n]{a_{1}+a_{2}+\cdots+a_{n}}}=1$ if $\displaystyle \varlimsup_{n\rightarrow\infty}{\sqrt[n]{a_{n}}}=1$ 11 Prove that $f(x)$ be a constant 10 Evaluate $\int_{0}^{1}{\frac{\ln{x}}{x^2-x-1}dx}$ 9 Find the limit of $\lim_{n\to\infty}\frac{n}{\ln{n}}\left(\frac{1}{p+1}-na_{n}^{p+1}\right)$

593 Reputation

 +20 prove $f(\sqrt{2})\geq 0$ related $(g(x)f'(x))'+f(x)\geq 0$ +35 Find the limit of $\lim_{n\to\infty}\frac{n}{\ln{n}}\left(\frac{1}{p+1}-na_{n}^{p+1}\right)$ +10 Show that $P_{n}(x)\rightrightarrows 0\qquad (x\in[0,1])$ +5 Limit related to the recursion $a_{n+1}=(1-n^{-1/4}a_n)a_n$

 3 Prove $a\sqrt[3]{a+b}+b\sqrt[3]{b+c}+c\sqrt[3]{c+a} \ge 3 \sqrt[3]2$ 2 proving :$\frac{ab}{a^2+3b^2}+\frac{cb}{b^2+3c^2}+\frac{ac}{c^2+3a^2}\le\frac{3}{4}$. 2 Prove that $\int_{0}^{1}{f^{2}(x)dx}\leq \frac{4}{3}\left(\int_{0}^{1}{f(x)dx}\right)^2$ 2 Showing that: $(\frac{a}{b+c})^2+(\frac{b}{a+c})^2+(\frac{c}{a+b})^2+\frac{10abc}{(a+b)(b+c)(c+a)}\ge 2$ 2 Prove that $\frac 1 {x+y}+\frac 1 {y+z}+\frac 1 {z+x}\geq \frac 5 2$.

10 Tags

 9 inequality × 4 0 polynomials 2 calculus × 20 0 proof-verification 0 integration × 2 0 real-analysis 0 limits 0 recurrence-relations 0 linear-algebra 0 definite-integrals

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