Test 3 Review
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     Part I ( Multiple choice)

     1. Use the root (ratio) test to determine whether the series 
        is absolutely convergent, conditionally convergent, or divergent.

        WW. 8.4, 1- 6

        lim |a_(n+1)/a_n | as n --> infinity
 
        |a_n|^(1/n) --> s < 1 ==> the series is convergent.        
             n --> infinity  

     2. Use the geometric series 

         (1-x)^(-1) 1 + x + x^2 + x^3 + . . .

        for |x| < 1  
      to determine the power series representation of the function f(x)=b/(a-x).

 
        WW. 8.6, 1-3

       

     3. Write the Taylor expansion for f(x) about x = a.

        WW. 8.7, 7, 15 

     4. Eliminate the parameter t to find the Cartesian equation of the curve

      WW. 9.1, 1-6


     5. Find the largest interval of convergence for a power series.
        
        WW. 8.5, 1-3
     

     6. Find the MacLAurin series of f(x).


       WW. 8.7. 1, 5, 8

     7. Use Maclaurin series for f(x) (family of 1/(1-x)) to obtain the Maclaurin series for the function f(x).
                 
        WW. 8.6, 5, 6, 8 


     8. Find a parametrization for a given circle 

        WW. 9.1, 9, 10 


                  

         Part II (Free response)
         -----------------------

   1. Given a power series
            
          c_0 + c_1 (x-p) + c_2 (x-p)^2 + c_3 (x-p)^3 + ...


     (a) What is the largest interval of convergence?


     (b) What is the radius of convergnece?

       WW.8.5, 4, 6, 9      



   2. Find the Taylor expansion for f(x) 

            WW. 8.7, 3, 7    


   3. For the parametric curve defined by (x(t), y(t)) 
       algebraically  find the equation of the tangent line to the curve at t = a.       


       WW. 9.2, 1, 5