01
Maclaurin series
For each of these functions, find the Maclaurin series.
(a)
(b)
02
Maclaurin series
For each of these functions, find the Maclaurin series.
(a)
(b)
03
Taylor series of
Find the Taylor series for the function
centered at .
04
Discovering the function from its Maclaurin series
For each of these series, identify the function of which it is the Maclaurin series.
(a)
(b)
05
Discovering 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)
06
Summing 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.)
07
Data of a Taylor series
Assume that
, , , and . Find the first four terms of the Taylor series of
centered at .
08
Evaluating series
Find the total sums for these series:
(a)
(b)
09
Large 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 .)