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:**

Six questions which involve computing Taylor Series expansions of logarithmic and trigonometric functions.

18.01

*Single Variable Calculus*, Fall 2005

Prof. Jason Starr

**Course Material Related to This Topic:**

- Complete exam problem problems 9.1 to 9.6 on page 6
- Check solution to exam problems 9.1 to 9.6 on page 6

Two questions that involve finding the Taylor series for √(1+x) and the inverse tangent function.

18.01

*Single Variable Calculus*, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problem problems 18 to 19 on page 2
- Check solution to exam problems 18 to 19 on page 1

Three multi-part questions which involve finding power series for various trigonometric, exponential, logarithmic, and rational functions, in additional to finding the radius of convergence and evaluating four limits using power series.

18.01 Single Variable Calculus, Fall 2006

Prof. David Jerison

**Course Material Related to This Topic:**

- Complete exam problems 7D-1 to 7D-3 on page 45
- Check solution to exam problems on pages 102–4