please help, i dont know how to post on latex, for example the attachment is on the link below but I dont know how to post on this message
Just surround your $\displaystyle \text\LaTeX$ code with [tex] and [/tex]. The board sets math mode automatically, so don't use dollar signs around everything.
For example:
ProducesCode:[tex]\sum_{n=1}^\infty\frac1n=\frac{\pi^2}6[/tex]
$\displaystyle \sum_{n=1}^\infty\frac1{n^2}=\frac{\pi^2}6$
Use \text{} to get regular non-math text. There are limits on the number of characters and the size of each $\displaystyle \text\LaTeX$ image, so you may need to break things up into several sections. For full paragraphs of text, like in your PDF, post the non-math text outside of the [tex] tags.
Find the least upper bound and the greatest lower bound of the following sets. For a given $\displaystyle \epsilon$>0, find a number in the set that exceeds (l.u.b.A)-$\displaystyle \epsilon$ and a number in the set that is smaller than (g.l.b. A)+ $\displaystyle \epsilon$.
(a). A=$\displaystyle \lbrace
$$\displaystyle \frac{4+x}{x}$$\displaystyle \vert$x
$\displaystyle \geq$
1$\displaystyle \rbrace$
So, for the record, the actual question that the OP wants an answer for is:
l.u.b. = 5, g.l.b. = 1. Do you see why?Find the least upper bound and the greatest lower bound of the following sets. For a given $\displaystyle \epsilon$>0, find a number in the set that exceeds (l.u.b.A)-$\displaystyle \epsilon$ and a number in the set that is smaller than (g.l.b. A)+ $\displaystyle \epsilon$.
$\displaystyle \text A=\left\{\left.\frac{4+x}x\;\right\vert\;x\geq1\ri ght\}$