Integration and differentiation of power series

The  exercise appears under the Integral calculus Math Mission. This exercise creates power series from a given power series by derivatives and integrals.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the derivative or antiderivative of the power series: This problem provides a power series that is being either differentiated or integrated. The student is asked to find the solution to the derivative or integral and indicate the correct answer.Iadops1.png

Strategies
Knowledge of the power rule for derivatives and the power rule for integrals are encouraged to ensure success on this exercise.
 * 1) The derivative or integral of a power series can be found by integrating or differentiating each term separately. Therefore one needs only to work with the general term for determining the solution.

Real-life Applications

 * 1) Real-life situations are not "exact" so approximating functions are used as models of real-life behavior in the sciences and economics. These concepts are used to create those approximating functions.
 * 2) Being able to manipulate something given into something needed is a common theme in mathematics.