Math 106-01: Calculus II: Reading Homework 9.1

1. Approximations and Series : what is this chapter about? what types of approximations might we consider?
   
   1. Taylor Polynomials : what do Taylor polynomials do?
      
      1. linear approximations : what is the Taylor polynomial of degree 1?
         
      2. quadratic approximations : how are the coefficients of a quadratic approximation to a function determined? what is the taylor polynomial of degree 2 approximating a function about x=0?
         
      3. higher-degree polynomials : how are higher degree Taylor polynomials formed?
         
      4. points other than x=0 : how does a Taylor polynomial change if we approximate the function near x=a instead of x=0?
         
   2. Taylor Series : what is a Taylor series?
      
      1. specific functions : what are the Taylor series for sin(x), cos(x), and e^x?