High School Math : Taylor and Maclaurin Series

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #81 : Calculus Ii — Integrals

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 #1 : Taylor And Maclaurin 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 

Example Question #1 : Understanding Maclaurin Series

Give the  term of the Maclaurin series expansion of the function .

Possible Answers:

Correct answer:

Explanation:

This can most easily be answered by recalling that the Maclaurin series for  is 

Multiply by  to get:

 

The  term is therefore .

Example Question #1 : Taylor And Maclaurin Series

Give the  term of the Maclaurin series of the function  .

Possible Answers:

Correct answer:

Explanation:

The  term of a Maclaurin series expansion has coefficient

.

We can find  by differentiating three times in succession:

The term we want is therefore

Example Question #1 : Applying Taylor Series

Give the  term of the Maclaurin series expansion of the function .

Possible Answers:

Correct answer:

Explanation:

The  term of a Maclaurin series expansion has coefficient

.

We can find  by differentiating twice in succession:

 

 

The coefficient we want is 

,

so the corresponding term is .

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