| Finding taylor series | |
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| Description | |
| Exercise Name: | Finding taylor series |
| Math Missions: | Integral calculus Math Mission |
| Types of Problems: | 3 |
The Finding taylor series exercise appears under the Integral calculus Math Mission. This exercise involves finding Taylor series using the definition.
Types of Problems[]
There are three types of problems in this exercise:
- What are the first four nonzero terms of the Taylor series?: This problem gives four Taylor series, and asks for the first four nonzero terms. The user is required to find out what these are and write it in the space below.
What are the first four nonzero terms?
- What is the coefficient of the term containing the given expression?: This problem asks the user to find out the coefficient for the term containing the given expression of the Taylor polynomial.
What is the coefficient for the term?
- Which of the following is the second degree Taylor polynomial?: This term gives several choices to choose from when it asks for the second degree Taylor polynomial.
Which is the second degree Taylor polynomial?
Strategies[]
- It is important to know how to solve Taylor series for success while doing this exercise.
Real-life Applications[]
- There are also applications in physics. If a system under a conservative force (one with an energy function associated with it, like gravity or electrostatic force) is at a stable equilibrium point x 0, then there are no net forces and the energy function is concave upwards (the energy being higher on either side is essentially what makes it stable).