Math 106-01: Calculus II: Reading Homework 7.6

1. Approximation Errors and Simpson's Rule : what is true about the errors in a numerical approximation?
   
   1. Error : what is error?
      
      1. LHS and RHS : how does the error for a left- or right-hand sum decrease with increasing n? what is the consequence of this if we want a highly accurate result?
         
      2. Trapezoid and Midpoint Rules : how does error in the trapezoid and midpoint rules decrease with increasing n? what is the effect on the accuracy if 10 times as more subdivisions are used?
         
   2. Simpson's Rule : how is Simpson's rule arrived at? what is Simpson's rule?
      
      1. error : how does accuracy improve with increasing n in Simpson's rule?
         
   3. Other considerations : how does the book consider the error in the different rules from an analytical viewpoing?
      
      1. Integrands : how may the integrand affect the error in a numerical calculation?