MATH 134

Problem Set 6 Grading Instructions: 

   Section 8.2/11 -- 4 points (2 for set-up of integral, 2 for value)
               40 -- 6 points (2 for set-up of arclength integral, 1 
                               for other sides of figure, 3 for value.
                               Note: they will need to use a numerical
                               method here for arclength, probably Maple.
                               Any method (LEFT,RIGHT,MID,TRAP,SIMPSON),
                               OK, but point out that SIMPSON would be
                               be best choice if they don't use it.)
               41 -- 4 points (2 for set-up of integral, 2 for value;
                               this is one where 1 + (f'(x))^2 is another
                               perfect square)
               
             
              
   Section 8.4/1 -- 4 points (2 for set-up of integral, 2 for value)
               6 -- 6 points (2 for part a; 4 for part b.  This is another
                              one where the integral must be done with a
                              numerical method)
              10 -- 10 points (2 for a, 4 for b, 4 for c.  Note in c,
                               they need to solve an equation 
                               x - ln(1+x) = A.  The solution says A is 
                               about 5000; a more accurate value is
                               4995.39.  If the more accurate value is
                               used the value of x changes too.  So
                               don't take off for x anywhere between
                               4900 and 5100.)
              12 -- 2 points
              18 -- 4 points  (2 for mass, 2 for x-coord of center of mass)
              21 -- 6 points  (2 for part a, 4 for b. Point out that part
                               a can  be answered just by noting the density
                               is increasing with x if they don't do it that
                               way)
   
   Section 8.7/1 -- 4 points (for pdf, any graph with one hump toward middle 
                              is OK; cdf should look something like an
                              antiderivative of what they give)
               2 -- 4 points (any graph that decreases as x increases OK for 
                              pdf)
               3 -- 4 points (any graph with two humps and a min in
                              between is OK for pdf)
               8 -- 4 points (1 for "cdf", 1 for value of c, 2 for graph of 
                              pdf)
                              
               9 -- 4 points (1 for "pdf", 1 for value of c, 2 for graph of
                              cdf.  Look for correct concavities here)
                              
              10 -- 2 points (Full credit for anything like "No, because
                              the thin tall spike doesn't contain much area")
              
   Section 8.8/4 -- 4 points (2 each part)
               5 -- 6 points (2 each part)
               6 -- 8 points (2 each part) 
              
   Total:  86 points
   
   Note:  We have an exam coming up next Friday that includes this 
          material, so please try to get this back by Tuesday next 
          week.  Thanks, Rosie!