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Mathematical Expression Editor
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Exercises relating to Taylor series and their computation.
Use the Maclaurin series for to give a complete formula for the Maclaurin series for :
Use the Maclaurin series for and to give a complete formula for the Maclaurin
series for :
Your formula should account for the fact that there are only even powers
of .
Compute the Taylor series of the function centered at the point .
Compute the Maclaurin series of the function identified below.
Sample Quiz Questions
Compute the first nonzero terms in the Taylor series at of the function
Compute the series in stages beginning with substitution into known series:
Compute the first nonzero terms in the Taylor series at of the function
Compute the series in stages beginning with substitution into known series:
Sample Exam Questions
The first few nonzero terms of the Maclaurin series for are:
(Hints will not be revealed until you choose your response.)
The first few derivatives
of are:
Evaluating at gives , , , and . Therefore the series starts with the terms
.
Find the Taylor polynomial of degree 2 for centered at .
Use the Taylor polynomial of degree for centered at to approximate the value of .
Let be the unique function that satisfies , , and for all . Find the Taylor Series of
centered at .
Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)