Analytic functions and Taylor series are defined, including the concept of an infinitely differentiable function.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Step-by-step method for computing a Taylor series, with example of finding the Taylor series expansion of f(x) = (1-x)^{-1} about x = 0.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Taylor series expansions of (1-x)^{-1}, e^{x}, sin(x), and cos(x) about any point x=a.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

Five questions which involve Taylor series approximations for sine, cosine, exponential, logarithmic, and other functions, as well as finding error bounds on these approximations.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 7C-1 to 7C-5 on page 44
- Check solution to exam problems 7C-1 to 7C-5 on pages 100–2