Manipulating Taylor Series

Algorithm for Computing Taylor Series

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:

• Read lecture notes, section 3 on pages 4–5

More Examples of Taylor Series

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:

• Read lecture notes, section 4 on pages 5–9

Taylor Series

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

General Power Series

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