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Mathzsltidgssfunlamwtllhenfakh: Tf g B alms an Laid & diftnttkmlaib )
,adif g
'
is , ntgrbkm laid,then
fabg'
= glbl -gl . ) .
idea : Fm the MVT,
we hnoglbtgbttjko ) ( b - a) fr se xoekih ) .
y=gk)y=jk)
of dim%
Btnaethkfthgaprttn P={ at tonic . . . ctitd. Wear write
glbtgktgltntgltn . , )tgK . ,) -gltn . a) t. . . tgltdglt , ) tgltitglt . )
And new ahgltitglti . D= gllxilltitii ) frsexieltiniti )
y=gk)y=jk)
••
My .
.
.Amaker¥,
1 ¥,
1 My'm I tfg
t , tz t} tq
t , tz +3 £4
But nw the part is tht if the swbrwkmbmteprtitmaesmll, jlxiltti - tin ) a Mlg ,Hiatt ) ltitit )
& jlxillti - tin ) amlg ,Hiatt ) ltitit )
So nw Us mhe this rigorous :
Proof: Wehw g is mtgrke
,so S!g' = Ubs' )=hf{Ulgip) : Papotkf GD } & alsofitlg't=sp{Lljip ) :
Papqtlyfg
fufe ,
if neanslwtht Lbipkglbtgkkuls:P) frallprtksp,
than it mtfllwlht
Llgltglbtgk) IUlj ).
Bt then we hwthtg '
B mtgrtk,so
Lljlttlg'), majtht both regality not be qnlitg & we he
gc4. GGI .
- UgD=Ub ' ) =)! j
so ht p={ a to < t,L
. .
.< tits be a prttm .
Then freahsknlwl Ctirti ),
the Man the fresh gates
F xieltinti ) s.it . jlxit stylist or. quirky , gltitglti D= jlxiltti - tin )
.
Now,tydefinitn mlg
'
,Hint :] ) ± gtxilt Mls : Hi . it :] ) . so
Llj # = .±f,
mlg'
,Hint :DHi - ti . i ) t Fe glxilltiti . D E ZMIG '
,Hi . itD) Hi - ti . ,) = UH
,P) .
Bt new §,
gtxiltti . to D= In lgttil -
glti.it#iJHoDHgHA.Hi)t...HgHnX-gtkDHgltntgVniD=gltntglto)=glbtgk
).
so we indeed he Lljpkglbtgkktllsip) t P,so glbtgla) = £9 '
, as desired. x#