The domain of f is all real numbers except
points at which q is zero Since polynomial functions are continuous (Example 14), f is
continuous by (4) of  Theorem 1 Example 17 Discuss the continuity of sine function Solution To see this we use the following facts
0
lim sin
0
x
x
→
=
We have not proved it, but is intuitively clear from the graph of sin x near 0