worksheet 1 what is the difference between a taylor series a maclaurin
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Question
Worksheet
1. What is the difference between a Taylor series, a Maclaurin series, and a power series?
2. Find the Maclaurin series for f(x) = 3x² cos(5x).
3. Find the Maclaurin series for the derivative of 3x² cos(5x). (Hint: Use the answer above
and find the deriviative of the series for 3x² cos(5x).)
4. Find the Maclaurin series for f 3x² cos(5x) dx. 5. Find the first 3 terms of the Maclaurin series for f(x)
=
√√√x +4.
6. Find the first 4 terms of the Taylor series for f(x) = x ln x centered about a =
2.
7. If f(x):
=
k=0
5k
k!
xk, what is f"(0)?
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