High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #2251 : High School Math

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 : Understanding 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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