The** Maclaurin series for sin x, cos x, and e^x **exercise appears under the Integral Calculus math section on Khan Academy. This exercise shows you how to turn a function into a power series.

## Types of ProblemsEdit

There are five types of problems in this exercise:

1. *Determine the first three non-zero terms of the Maclaurin polynomial: *The student is asked to find the first three non-zero terms of the Maclaurin polynomial for the given function.

2. *Determine the sum of the infinite series given: *The student is asked to find the exact value of the sum of the infinite series given.

3. *Determine the value of the power series at the given point: *The student is asked to evaluate the power series at a given point.

4. *Determine what function evaluates to the given power series: *The

student is asked to match up the function that evaluates to the given power series.

5. *Determine the value of the point given the function: *The student is asked to find out the value of point using the Maclaurin series on the function.

## StrategiesEdit

Knowledge of taking derivatives, taking integrals, power series, and Maclaurin series are encouraged to ensure success on this exercise.

1. Maclaurin series: =

Ratio =

2. The Maclaurin series is a special case of the Taylor series.

3. The Maclaurin series of sine is:

=

4. The Maclaurin series of cosine is:

=

5. The Maclaurin series of e^x is:

=

6. Euler's formula:

=

7. Euler's identity:

8. Complex functions can be converted to power series by using substitution.

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