f(x) = tan 2.a = 0
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.4: Definition Of The Derivative
Problem 36E
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Question
Taylor series and interval of convergence
a. Use the definition of a Taylor/Maclaurin series to find the first four nonzero terms of the Taylor series for the given function centered at a.
b. Write the power series using summation notation.
c. Determine the interval of convergence of the series.
Expert Solution
Step 1
The given function is , a=0.
(a) To find: First four terms of Taylor's series/Maclaurin series centered at a.
(b) To Write: Power series using summation notation.
(c) To Determine: Interval of convergence.
Step 2
Taylor's series for a function f is given by,
(i)
.
,
,
,
,
.
.
.
.
.
Thus, From (i),
+...
these are the first four terms of Taylor's expansion of the function .
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