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 (e).  The composition  ,  provided that    is continuous in a neighborhood of the point  .

Solution 23 (e).

See text and/or instructor's solution manual.

Solution.  Given that    is continuous at the point    we have  ,   and

given that    is continuous at the point    we have  .

It follows that  .  

This solution is complements of the authors.

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