Exercise 18.  Show the following concerning the exponential map  .  

18 (e).  The image of the horizontal ray    is a ray.

Solution 18 (e).

See text and/or instructor's solution manual.

Solution.    .  

Substitute     into the equations    and    and obtain

                    .

This set is the parametric representation the ray  .

We are done.   

Aside.  We can let Mathematica double check our work.

                              The image the horizontal ray  ,  is the ray   .

This solution is complements of the authors.

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