This document contains exercises to prove properties of the function f(x) = 1/(x^2+1). The first exercise shows that f(x) = -x^2/(x^2+1)(f(x)+1) for all real numbers x. The second exercise shows that 0 < f(x)+1 ≤ 1 for all real x. The third exercise uses the epsilon-delta definition of limits to show that the limit of f(x) as x approaches 0 equals 1.