High School Math : Understanding Taylor Series

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Understanding Taylor Series

Give the   term of the Maclaurin series of the function 

Possible Answers:

Correct answer:

Explanation:

The   term of the Maclaurin series of a function  has coefficient

The second derivative of  can be found as follows:

The coeficient of  in the Maclaurin series is therefore

Example Question #2 : Understanding Taylor Series

Give the   term of the Taylor series expansion of the function  about .

Possible Answers:

Correct answer:

Explanation:

The  term of a Taylor series expansion about  is

.

We can find  by differentiating twice in succession:

 

 

so the  term is 

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