Worksheet: Maclaurin and Taylor Series of Common Functions
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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Q4:
The function can be represented by the power series . Use the first two terms of this series to find an approximate value of to 2 decimal places.
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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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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Q8:
Use the Maclaurin series of to express as an infinite 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 1 in ascending powers of .
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Q11:
Write the first three terms of the Taylor expansion for about in ascending powers of .
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Q12:
By writing the first three nonzero terms of the Taylor expansion of about in ascending powers of , estimate the value of . Give your answer accurate to three significant figures.
Q13:
By writing the first three nonzero terms of the Maclaurin expansion of in ascending powers of , estimate the value of . Give your answer accurate to three significant figures.
Q14:
Find the first three nonzero terms of the Taylor expansion for about , in ascending powers of .
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