Science:Math Exam Resources/Courses/MATH100/December 2015/Question 10 (c)/Solution 1
When , the linear functions and become very large, however the exponential function decays very faster and becomes zero, therefore
Indeed, more rigorously, it follows from L'Hospital's rule:
On the other hand, when , using the graph of the functions we can easily see that
Therefore, has a horizontal asymtote only when which is at the very end of positive x-axis.