All High School Math Resources
Example Questions
Example Question #1 : Taylor And Maclaurin Series
Give the term of the Maclaurin series of the function
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 : Taylor And Maclaurin Series
Give the term of the Taylor series expansion of the function about .
The term of a Taylor series expansion about is
.
We can find by differentiating twice in succession:
so the term is
Example Question #3 : Taylor And Maclaurin Series
Give the term of the Maclaurin series expansion of the function .
This can most easily be answered by recalling that the Maclaurin series for is
Multiply by to get:
The term is therefore .
Example Question #4 : Taylor And Maclaurin Series
Give the term of the Maclaurin series of the function .
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 .
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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