6. If af/dx is continuous on the rectangle R = {(t, æ) : 0 0 such that |f(t, x1) – f(t, x2)|

Extracted text: 6. If af/dx is continuous on the rectangle R = {(t, æ) : 0 < |t="" –="" tol="">< a,="" 0="">< |æ="" –="" xo]="">< b},="" prove="" that="" there="" exists="" a="" k=""> 0 such that |f(t, x1) – f(t, x2)| < k\x1="" –="" x2|="" for="" all="" (t,="" æ1)="" and="" (t,="" x2)="" in="" r.="" 7.="" define="" the="" sequence="" {un}="" by="" uo="" (t)="20," un+1="x0" +="" to="" +="" f(s,="" un(8))="" ds,="" п="" %3="" 1,2,....="" use="" the="" result="" of="" the="" previous="" exercise="" to="" show="" that="" |f(t,="" un="" (t))="" –="" f(t,="" un-1="" (t))|="">< k|u,(t)="" –="">