Given a function F let us say that the silly limit of F at a is L if there is some \delta>0 \text { such that for } \text {

every } \epsilon>0 \text { if } 0<|x-a|<\delta \text { then }|F(x)-L|<\epsilon If this holds, then we will say that the silly limit of F exists at a. 1. Prove that even for the function g defined g(x) = x there is no point at which the silly limit of g exists. 2. Find a function for which the silly limit does exist at some point.