Let f (a,b) R is a bounded function and c E (a, b). Show that the...

 

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Let f (a,b) R is a bounded function and c E (a, b). Show that the two notions of lim supe. xx f(x) A = sup{a alim f(x); liman = c}. n k B = lim f(x), sup n Ele-1/nc+1/n] coincide. That is, prove that A = B. Let f (a,b) R is a bounded function and c E (a, b). Show that the two notions of lim supe. xx f(x) A = sup{a alim f(x); liman = c}. n k B = lim f(x), sup n Ele-1/nc+1/n] coincide. That is, prove that A = B.

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To prove that the two notions of lim sup coincide we need to show that lim sup fx as x approaches c ... View the full answer