## 6.3. Discontinuous Functions

### Examples 6.3.8(a):

f(x) = exp(1/x) |

As *x* approaches zero from the right, *1/x*
approaches positive infinity. Therefore, the limit of
*f(x)* as *x* approaches zero from the right
is positive infinity.

As *x* approaches zero from the left, *1/x* approaches
negative infinity. Therefore, the limit of
*f(x)* as *x* approaches zero from the left
is zero.

Since the right-handed limit fails to exist, the function has an essential discontinuity at zero.