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01:640:152
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Lecture 12

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Rutgers University

Mathematics

01:640:152

Noone

Spring

Description

Ex power series Representation for I-x) on GI, y
Find a with
since it's a G.S
th a
G. S
Therefore
when we intigrate both sides ln -xl x t
et r o
Taylor Maclauren Series
at "c
se A has a power series representation
Supp
a a
st at 11c FT CC)
Derivative of f e
Then
a
man x-c)
n-2
n
n
3.2. la a t 4.3.2. Ex-c) t S. 4.30
Cac-cy
Then, FCX)
cy becomes
cx-en. Taylor Series
n
This is the Taylor Series
IA c o, This becomes Maclaurin Series
mao n
r Series cut c o
Ex Acxy e Find Te
Step
1: Find derivatieve of Fancl look. Fore patem
Step 2 Plug
n r C.
F C
For FCX) e
Step 3: Set up
Step 4
Interval of Convergence
O
Interval of convergence
Ratio Test: lim
or G
Fur ex can be represented by RT on Goo
oo)
Find the taylor Series
Aor PCx
in pc at c
Ex: 4.3.2
3.2
F C.
p''CI)
(nt
n E o
DC
Ratio Test: lim
odd number always o x 2.
nt
End
Harmonic Series
C-1)
.-L verging Alternatin
Harmoni
Serie

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