problems see the attach files, thanks for helping me!

\fProblem 2. Let HI} ha a continuous. function on [I], 00) Suppose that x} 3% G far all I T;- U and that \"(ENE = ELEtjdt for all .1: E i]. Prove that x] = I for all I 2 . \fProblem 6. Consider the system of equations 1:2 1J2 tu2 f[u,v,z,y,z,w] 21:2 +1:2 +1ng 29= I], g[n,v,1,y,z,w] = F + E + E 1T=. Prove that for M = (Iujynjzn1w = (2,1,1,2] E 12". there is a ball B,(M} 5 st and di'erentinble functions n[:,y, 2:,nr} and 1.!(I, gnaw} such that u(M} 2 1, 1.?{M} = 3 and fl:{-Ts y: E, I\"): \"[3: y: Z, w]... 1719'\"; 31 w} = 3(u{$:y1 31w)5{35y135w}1 1': 1'53an 2 JI: all [m,y,z,w] E B,[M}