1. Find the horizontal asymptotes of the graph of the function $$g(x) = \frac{|f(x)|}{x-2}$$ if $$f(x)$$ satisfies inequality $$f(x+1) \le x \le f(x)+1$$ for every real $$x$$.
2. Let $$f: R->R$$ be a function that is differentiable at zero and such that $$f(0) = 0$$. Show that for each...