tan-x = E(-Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function.f (x) =V16 + a?r3(-1)" 1.3.5..... (2n + 1)2n .4" . n!n=1* (-1)"1.3. 5..... (2n – 1)2n . 16" . n!+2np3* (-1)" 1.3 -5..... (2n – 1)2n+3+4n=12". 16" . n!(-1)"1.3.5.... . (2n – 1)4732n . 16" - n!g³ (-1)" 1·3.5.... · (2n +1)2n . 47 . n!2=1" = 1 + x + x? + x' + ...R = 11 - xx²+2!R = 001!x 2n+1sin x = E(-1)"+R = 00(2n + 1)!3!5!n-0x 2m= 1 -(2n)!x?cos x =(-1)"R = 002!4!6!x2n+1xx'(-1)"R = 12n + 13k(k – 1).k(k – 1)(k – 2).(1 + x)* =x" = 1 + kx +-x² +2!x' +...R = 13!Need Help?Read ItWatch It

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Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function. f (x) = V16 + r (-1)" 1 - 3 - 5 - ... (2n +1) 2" - 4" . n! (-1)"1 - 3 - 5 - ... (2n – 1) 2" - 16" · n! 2n (-1)" 1 -3 - 5 - ...· (2n – 1) 2" . 16" - n! 2n+3 * (-1)" 1.3.5.... . (2n – 1) 2m . 16" · n! *(-1)"1- 3 - 5 . ... - (2n + 1) 2n . 4" . n! 1 + x + x² + x' + · .. R- 1 e R= 00 2001 sin x- R- 00 (2n + 1)! 5! cos x- 2-1)* (2n)! =1 - R= 00 4! 6! tan-x - -1)" R- 1 +... -()-- • k(k – 1) „2 4 k(k – D)(k – 2) qɔ + ... R=1 (1 + x)* - =1+ kr + 3! Need Help? Read It Watch It

Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function. f (x) = V16 + r (-1)" 1 - 3 - 5 - ... (2n +1) 2" - 4" . n! (-1)"1 - 3 - 5 - ... (2n – 1) 2" - 16" · n! 2n (-1)" 1 -3 - 5 - ...· (2n – 1) 2" . 16" - n! 2n+3 * (-1)" 1.3.5.... . (2n – 1) 2m . 16" · n! (-1)"1- 3 - 5 . ... - (2n + 1) 2n . 4" . n! 1 + x + x² + x' + · .. R- 1 e R= 00 2001 sin x- R- 00 (2n + 1)! 5! cos x- 2-1) (2n)! =1 - R= 00 4! 6! tan-x - -1)" R- 1 +... -()-- • k(k – 1) „2 4 k(k – D)(k – 2) qɔ + ... R=1 (1 + x)* - =1+ kr + 3! Need Help? Read It Watch It

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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tan-x = E(-
Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function.
f (x) =
V16 + a?
r3
(-1)" 1.3.5..... (2n + 1)
2n .4" . n!
n=1
* (-1)"1.3. 5..... (2n – 1)
2n . 16" . n!
+
2n
p3
* (-1)" 1.3 -5..... (2n – 1)
2n+3
+
4
n=1
2". 16" . n!
(-1)"1.3.5.... . (2n – 1)
4
73
2n . 16" - n!
g³ (-1)" 1·3.5.... · (2n +1)
2n . 47 . n!
2=1
" = 1 + x + x? + x' + ...
R = 1
1 - x
x²
+
2!
R = 00
1!
x 2n+1
sin x = E(-1)"
+
R = 00
(2n + 1)!
3!
5!
n-0
x 2m
= 1 -
(2n)!
x?
cos x =
(-1)"
R = 00
2!
4!
6!
x2n+1
x
x'
(-1)"
R = 1
2n + 1
3
k(k – 1).
k(k – 1)(k – 2).
(1 + x)* =
x" = 1 + kx +
-x² +
2!
x' +...
R = 1
3!
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