- The function is the sum of three functions, all of them continuous on the interval ; thus is continuous on , by Theorem cont sum;
- ;
- .

- The function is continuous on , by Theorem cont sum;.
- .
- .

- (i)
- the function is continuous on ;
- (ii)
- the function has a limit on the right at (eventually infinite);
- (iii)
- the function has a limit on the left at (eventually infinite);
- (iv)
- these limts have different signs.

The graph of is diplayed in Figure 10.

Noah Dana-Picard 2007-12-28