## 6.3. Discontinuous Functions

### Examples 6.3.4(a):

We can easily check (by factoring the numerator) that the limit as*x*approaches

*3*from the right and from the left is equal to

*6*. Hence, the limit as

*x*approaches

*3*exists, and therefore the function has a removable discontinuity at

*x = 3*. If we define

*k(3) = 6*instead of

*k(3) = 1*then the function, in fact, will be continuous on the real line.