Stepwise problems - Thu. 11:59pm
Tayler and Maclaurin series
01
01
Link to originalMaclaurin series
For each of these functions, find the Maclaurin series.
(a)
(b)
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04
Link to originalDiscovering the function from its Maclaurin series
For each of these series, identify the function of which it is the Maclaurin series.
(a)
(b)
Applications of Taylor series
03
01
Link to originalApproximating
Using the series representation of
, show that: Now use the alternating series error bound to approximate
to an error within .
Regular problems - Sun. 11:59pm
Tayler and Maclaurin series
04
02
Link to originalMaclaurin series
For each of these functions, find the Maclaurin series.
(a)
(b)
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03
Link to originalTaylor series of
Find the Taylor series for the function
centered at .
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05
Link to originalDiscovering the function from its Maclaurin series
For each of these series, identify the function of which it is the Maclaurin series, and evaluate the function at an appropriate choice of
to find the total sum for the series. (a)
(b) (c)
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06
Link to originalSumming a Maclaurin series by guessing its function
For each of these series, identify the function of which it is the Maclaurin series:
(a)
(b) Now find the total sums for these series:
(c)
(d) (Hint: for (c)-(d), do the process in (a)-(b), then evaluate the resulting function somewhere.)
08
07
Link to originalData of a Taylor series
Assume that
, , , and . Find the first four terms of the Taylor series of
centered at .
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08
Link to originalEvaluating series
Find the total sums for these series:
(a)
(b)
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09
Link to originalLarge derivative at
using pattern of Maclaurin series Consider the function
. Find the value of . (Hint: find the rule for coefficients of the Maclaurin series of
and then plug in .)
Applications of Taylor series
11
02
Link to originalSome estimates using series
For each of these estimates, use the error bound formula for alternating series.
Without a calculator, estimate
(angle in radians) with an error below .
12
03
Link to originalSome estimates using series
For each of these estimates, use the error bound formula for alternating series.
Find an infinite series representation of
and then use your series to estimate this integral to within an error of .