For $S = \{ \frac{4x}{x+1} | x \in \mathbb{R}, x \geq 1 \}$ bdd? g.l.b.S? l.u.b.S? Let $S = \{ \frac{4x}{x+1} | x \in \mathbb{R}, x \geq 1 \}$
Is S bounded? Find g.l.b. S and the l.u.b. S if they exist. Give justification, formal proof not necessary. (Based on Calculus)
I did not justify my answers for this, but i knew the glb S = 2
and lub S = DNE.  
I also said based off calculus that because 4x is faster than x+1 that it is unbounded above.

You can write $\frac{4x}{x+1}=\frac{4}{1+\frac{1}{x}}$, then on the interval $[0,\infty)$, the set $S$ is bounded below by zero and bounded above by four. 
