Question

By considering different paths of approach, show that the function has no limit as ________?

Answer 1

The function has no limit as x approaches zero.

Step-by-step explanation:

The function has no limit as x approaches zero. Consider the function y = 1/x. As x approaches zero from the positive side, y approaches infinity. On the other hand, as x approaches zero from the negative side, y approaches negative infinity. Since the function approaches different values as x approaches zero, the limit does not exist.