5. Use "known" Maclaurin series to evaluate the following limits. 1+1/x² (a) lim x →0 (b) lim x→0 COS X tan -1 x4 Xxx COS X - x5 1x³ (c) Can you use these series to evaluate lim x→3/2 -1 tan X - x COS X - x5 -? If not, why not?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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5. Use "known" Maclaurin series to evaluate the following limits.
cos x −1+x²
x4
(a) lim
x→0
(b) lim
x→0
tan-1 X
X COS X
x5
13
(c) Can you use these series to evaluate lim
x+3/2
tan¯¹ x −
X COS X
X5
1
23
-? If not, why not?
Transcribed Image Text:5. Use "known" Maclaurin series to evaluate the following limits. cos x −1+x² x4 (a) lim x→0 (b) lim x→0 tan-1 X X COS X x5 13 (c) Can you use these series to evaluate lim x+3/2 tan¯¹ x − X COS X X5 1 23 -? If not, why not?
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