Question

0<|x-a|<\delta \text { then }|F(x)-L|<\epsilon Given a function F let us say that the crazy limit of F at a is L \text { if for every } \epsilon>0 \text

{ and every } \delta>0 \text { if } If this holds, then we will say that the crazy 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 crazy limit of g exists. 2. Find a function for which the crazy limit does exist at some point.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6