Examples.

  1. Find a power series for .
    Discussion [Using Flash] [Using Java]

  2. Find a power series for .
    Discussion [Using Flash] [Using Java]

Theorem. Suppose that the radius of convergence of the power series

is r > 0 then the function

is both differentiable and integrable on the interval (c - r, c + r).

Moreover,

In addition, the radius of convergence of these two power series is also r.

Examples.

  1. Find a power series for .
    Discussion [Using Flash] [Using Java]

  2. Find a power series for .
    Discussion [Using Flash] [Using Java]

  3. Find the derivative and the integral of the function .
    Discussion [Using Flash] [Using Java]

  4. Evaluate .
    Discussion [Using Flash] [Using Java]