(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A= (4+X)/X WHEN x≥1

Find the least upper bound and greatest lower bound of the following sets.for a given ε>0,

Find a number in the set that exceeds l.u.b. A - ε and a number in the set that is smaller than

g.l.b.A + ε

2. Relevant equations

does this make sense? is it a right way to attack this question?

3. The attempt at a solution

x≥1 → 1 ≥1/x → 0<1/x≤ 1

is we multiply by 4. →0 < (1/x)4 ≤4

then add one → 1 < (4/x)+1 ≤ 5.

thus 1 is G.l.b of A AND 5 l.u.b of A.

Find a number in the set that exceeds l.u.b. A - ε ....

LET 5 is the upper bound of A. (given)

suppose K is also the upper bound of A. → 5 ≤ K

Suppose this is not the case.AND K < 5.

5-K > 0

ε = 5-K > 0

K =5 -ε SO THAT there is a number X(ε) E A thus x(ε) > 5-ε = K

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# Homework Help: Proof l.u.b of A.

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