AP Calculus BC : Maclaurin Series for exponential and trigonometric functions

Study concepts, example questions & explanations for AP Calculus BC

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Example Questions

Example Question #1 : Maclaurin Series For Exponential And Trigonometric Functions

Write out the first three terms of the Taylor series about  for the following function:

Possible Answers:

Correct answer:


The Taylor series about x=a for a function is given by

For the first three terms (n=0, 1, 2) we must find the zeroth, first, and second derivative of the function. The zeroth derivative is just the function itself.

The derivatives were found using the following rules:

Now, using the above formula, write out the first three terms:

which simplified becomes


Example Question #61 : Taylor And Maclaurin Series

Find the Maclaurin Series of the function

up to the fifth degree.

Possible Answers:

Correct answer:


The formula for an i-th degree Maclaurin Polynomial is

For the fifth degree polynomial, we must evaluate the function up to its fifth derivative.


The summation becomes

And substituting for the values of the function and the first five derivative values, we get the Maclaurin Polynomial

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