This is last years test which

you may use for practice if you

wish.


                                     NAME____________________________________

                                     SCHOOL__________________________________


TEST 4                      Monday, April 27, 2007

Fax the test answers to:   Fax  515-294-5454

and also Snail Mail your test answers to:

Irvin Roy Hentzel
Department of Mathematics
432 Carver Hall
Iowa State University
Ames, Iowa 50011-2064


 1.    Name the curves.

       (a)  r = Cos[theta]         
                             _________________________________    

       (b)  r = 1 + Cos[theta]    
                             _________________________________    

       (c)  r = 2 + Cos[theta]     
                             _________________________________    

       (d)  r = theta                   
                             _________________________________    
 
       (e)  r theta = 1                 
                             _________________________________    

       (f)  r = Cos[2 theta]           
                             _________________________________    

             2
       (g)  r  = Cos[2 theta]         
                             _________________________________    



 2.   Find the length of the  parametric curve defined by
                     
                    
      x =  a ( t - Sin[t] )      y = a ( 1 - Cos[t] ) 

      0 <= t <= 2 Pi.


  

                       2     2
 3.   Find  dy/dx and d y/ dx  without eliminating the parameter.

              2                           2
      x =  -----------         y =  -------------        t =/= 0
                 2                            2
            1 + t                    t ( 1 + t  )


     






  4.   Change this polar equation to rectangular coordinates.

              2                         
             r =  a Cos[ 2 theta ] 





  5.  Find the points of intersection of the curves

                 r = 1 + Cos[2 theta]

                 r = 1 - Sin[2 theta]




   6.  Find the area of the inner loop of


                 r = 1 + Cos[ 1/2 theta ] 





   7.   Find the area of one leaf of 

        r = 16 Cos[8 theta]




    8.  Set up the integral for the arclength of the limacon   

        r = 1 + 2 Cos[theta]     0 <= theta <= 2 Pi.




     9.  Find the area inside  r = 7 + Sin[theta]


                              2
    10.  Find the slope of   r  =  Cos[2 theta]  when theta = Pi/6.