How do you solve 2? Please write clearly thank you!(The second picture is just a definition for little 'o' notation) ( やこ。X ニIn general,n-mメニ o(メ), ,f nomlim Xミ0it n-m >o.メニ o(x), ×→+o nem.luxa We know that eo<3 ASo lux =forやトe.alineSox^ =ocex)fora E IRauyThe Taylor enpansibn withe Peano RemaielerCem be conten.as(ーメ)o +[m す…) ( +C=マー>×。Algebra for olx"), x->0 .Oi o1x")+ ocx)x-20こo(×MナMx^. ocx") =O (xPf. Q Hene d what we need te prove :Leto4x(ス) )gex)> ocx"), x>0.e fre)こ0こoややC入Need to show.こDx min (r,w j7つ(メリやNew Section 2 Page 37つメmIn tact, li frx? t goa)e ftx)やつe gos leinメラーO, or1) + o. (o or 2)ニ For each of the following identities, write down the exact mathematical statement and prove it (we did one examplein the lecture).1. o(x")· o(x")= o(x"+m), x → 0.2. am . o(2")= o(æn+m), x → 0.

Please check step 2 and 3 for the solution.!

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Math

Advanced Math

How do you solve 2? Please write clearly thank you! (The second picture is just a definition for little 'o' notation

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.4: Logarithmic Functions

Problem 38E

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Question

How do you solve 2? Please write clearly thank you!

(The second picture is just a definition for little 'o' notation)

( や
こ。
X ニ
In general,
n-m
メニ o(メ), ,
f nom
lim X
ミ0
it n-m >o.
メニ o(x), ×→+o nem.
lux
a We know that e
o<3 A
So lux =
for
やトe.
a
lin
e
So
x^ =
ocex)
for
a E IR
auy
The Taylor enpansibn withe Peano Remaieler
Cem be conten.
as
(ーメ)
o +[m す…) ( +C=
マー>×。
Algebra for olx"), x->0 .
Oi o1x")+ ocx)
x-20
こo(×
MナM
x^. ocx") =
O (x
Pf. Q Hene d what we need te prove :
Let
o4x(ス) )
gex)> ocx"), x>0.
e fre)
こ0
こo
やや
C入
Need to show.
こD
x min (r,w j
7つ
(メリや
New Section 2 Page 3
7つ
メm
In tact, li frx? t goa)
e ftx)
やつ
e gos lein
メラー
O, or
1) + o. (o or 2)
ニ

For each of the following identities, write down the exact mathematical statement and prove it (we did one example
in the lecture).
1. o(x")· o(x")= o(x"+m), x → 0.
2. am . o(2")= o(æn+m), x → 0.

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