Lesson Worksheet: Maclaurin and Taylor Series of Common Functions Mathematics • Higher Education
In this worksheet, we will practice finding the Taylor/Maclaurin series representation of common functions such as exponential and trigonometric functions and binomial expansion.
Q1:
Consider .
Find a power series representation for .
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Find its interval of convergence.
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Q5:
Consider the binomial expansion for .
Which of the following expressions is its fourth term?
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What is the limit of the th term as tends to infinity?
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- E1
Hence, write in summation (or sigma) notation a series which is equal to the limit of as tends to infinity.
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What is the value of this series?
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Q9:
Find the Maclaurin series of .
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Q10:
Write the first three terms of the Taylor expansion for about in ascending powers of .
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