Exercise 5.  Let  ,  

where  ,  ,  ,  and  .  

Here    denotes the principal cube root function.  

5 (a).  Show that    is a branch of the multivalued cube root  .  

Solution 5 (a).

See text and/or instructor's solution manual.

Solution.  ,  so  

           

This shows that    is indeed a branch of the cube root function.  

This solution is complements of the authors.

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