A function f is continuous at the point if the following conditions are satisfied. 1. is defined.
2) exists.
3) .
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.
E) Continuous everywhere.

Question

A function f is continuous at the point  if the following conditions are satisfied. 1.  is defined.
2)  exists.
3)  .
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.  
E) Continuous everywhere.

Quizplus · Accepted Answer

At point C, the function is discontinuous because condition 3 is violated. The limit as x approaches C exists, but is not equal to f(C). Therefore, condition 3 (the limit of the function as x approaches the point must be equal to the value of the function at the point) is violated. 
At all other points, the function satisfies all three conditions for continuity, so it is continuous everywhere except at point C.

A Function F Is Continuous at the Point If