Math 105-02: Calculus I: Reading Homework 4.8

1. Linear Approximations and Limits : why and where is a tangent line a good approximation for a function?
   
   1. The Tangent Line Approximation : what is the equation of the tangent line? what is a local linearization of a function?
      
      1. local linearization and limits : how is local linearization used to calculate limits?
         
   2. L'Hopital's Rule : what is L'Hopital's rule? how does the book justify the result?
      
      1. L'Hopital's rule : what is the more general form of the rule? how is it different than the first form?
         
      2. more L'Hopital : in what other cases may the rule be used?
         
   3. Dominance : what do we mean if we say that one function dominates another? how can L'Hopital's rule be used to determine this?