Example 5.  First find Maclaurin expansions for    and    of order    and   ,  respectively.
Then experiment and find the order of approximation for their sum, product and quotient.  

Solution 5.

Then find the series for their sum.  

Then find the series for their product.  

Then find the series for their quotient.  

Interpret the quotient as the product of    and    and see what's happening.  

(c) John H. Mathews 2004