Exercise 23.  Verify the results of Theorem 2.4.   If and are continuous at the point , then use standard techniques to prove that the following functions are continuous at .

23 (c).  The product   .

Solution 23 (c).

See text and/or instructor's solution manual.

Solution.  To show that    is continuous, use Theorem 2.2 applied to the product of two functions.

Since    and    are continuous at the point    we have    and  .  Using equation (2-19) we have



which establishes that    is continuous.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell