Originally Posted by

**transgalactic** 1.prove or desprove by example:

a)

$\displaystyle sup\{\frac{[x]}{[x]+1}|x\geq0\}=1$

b)prove that $\displaystyle x^{3}$ 'uniformly' continuous in R

c)if f(x) monotonicly decreasing in $\displaystyle [0,\infty)$ and $\displaystyle lim_{x->\infty}=0$then f(x)>0 for $\displaystyle x\in[0,\infty)$

d)f,g are continues in [a,b] if $\displaystyle x\in[a,b] \int_{a}^{x}f(t)dt=\int_{a}^{x}g(t)dt$ then f=g in [a,b]

regarding the first one i couldnt find a value for which the supremum is 1