Use the Maclaurin Series for f(x) =e^x to answer the following questions:(a)Evaluate f(x) at x=iθand expand the first 8 terms of the series (n= 0 to n= 7). (b)Simplify the first 8 terms of the series and group together the real and imaginary parts of the series. (c)Look for a pattern for the real part and imaginary part of the series and write the Maclaurin Series for e^x as the sum of a real series and an imaginary series. (d)Using the sum of the real and imaginary series above write an identity for e^x
Use the Maclaurin Series for f(x) =e^x to answer the following questions:(a)Evaluate f(x) at x=iθand expand the first 8 terms of the series (n= 0 to n= 7). (b)Simplify the first 8 terms of the series and group together the real and imaginary parts of the series. (c)Look for a pattern for the real part and imaginary part of the series and write the Maclaurin Series for e^x as the sum of a real series and an imaginary series. (d)Using the sum of the real and imaginary series above write an identity for e^x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the Maclaurin Series for f(x) =e^x to answer the following questions:(a)Evaluate f(x) at x=iθand expand the first 8 terms of the series (n= 0 to n= 7).
(b)Simplify the first 8 terms of the series and group together the real and imaginary parts of the series.
(c)Look for a pattern for the real part and imaginary part of the series and write the Maclaurin Series for e^x as the sum of a real series and an imaginary series.
(d)Using the sum of the real and imaginary series above write an identity for e^x
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