Module 4 : Local / Global Maximum / Minimum and  Curve Sketching
Lecture 12 : Asymptoes [Section 12.1]
12.1.5
Example:
 

Consider the function
                      .
We can write
                      
and we have,
                      .
Hence, the line

is an oblique asymptote to

both from the left as well as from the right. Moreover,
                          ,
and therefore, is a vertical asymptote, both from left as well as from right. Since,
                         for all ,
the critical points of are given by
                       i.e., i.e., .
Next,
                      for all .

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