MathDB

4

Part of 2005 Unirea

Problems(2)

math constest 2

Source: Unirea

2/8/2005
Find all aa real number such that xn=n{an!}x_n=n\{an! \} is convergeant Gabriel Dospinescu
real analysisreal analysis unsolved
Math constest 1

Source: Unirea 2005

2/8/2005
a>0a>0 f:[−a,a]→Rf:[-a,a]\rightarrow R such that f′′f'' exist and Riemann-integrable suppose f(a)=f(−a)f(a)=f(-a) f′(−a)=f′(a)=a2 f'(-a)=f'(a)=a^2 Prove that 6a3≤∫−aaf′′(x)2dx6a^3\leq \int_{-a}^{a}{f''(x)}^2dx Study equality case ? Radu Miculescu
integrationinequalitiesparameterizationfunctionreal analysisreal analysis solved