Megan, 

      Here is the next MATH 136 problem set (number 8):

    * Section 6.6/1, 2, 6, 17, 20, 42, 43, 47, 48, 52 (use the formulas from 51).
    * Additional problem: A thin wire has the shape of the segment of the x-axis 
      from x = 0 to x = 2. Find the total mass of the wire and the location of 
      its center of mass if the mass density function of the wire is
          - d(x) = ex/4 at location x.
          - d(x) = square root(1 + x^2) at location x.
    * Section 6.4/8, 11, 17 (but use the midpoint Riemann sum instead of Simpson's Rule).
    * Section 7.1/2, 4, 5, 10, 14.


    Of these, please grade:

    6.6/1 -- 2 points for setting up the integral correctly, 2 for the value
             (4 total)

    6.6/6 -- 2 points for the integral, 2 for the value 

    6.6/17 -- 4 points (like 1) -- don't be too strict, though.  For instance
              if everything is OK in the integral except for a constant
              factor (like the density, or the gravitational acceleration), only
              take off 1 point

    6.6/42 -- 2 points (1 for the total moment, one for the center of mass)

    6.6/48 -- 8 points total -- 1 each for the set-up of the three integrals
              for the moments and the area, 1 each for evaluation of the integrals
              2 points for the two coordinates of the centroid

    6.4/8 -- 4 points (1 for y', 1 for the set up of the integral, 2 for evaluating)

    6.4/11 -- 4 points (distributed like for 6.4/8)

    7.1/2 --  2 points (they should just compute y' and show y' + 2y = 2 e^x)

    7.1/5 --  4 points (they should check each one, 1 point for each one
              identified correctly)

    7.1/10 -- 6 points (2 for each part)


    Thanks, and have a happy Thanksgiving!

                                                John Little