Co KRIGE'

DO CCL

Exercise 1 /9p

a) De 're 've 'e I - 3×2 i pent e = - 2 em - I ell, pence = I e - o

,

deliver null e en ±

①

b) g Cx ) = f ( K A) = - ¥3 . I - paine ⇒ que

des bn

IT

bn -

- ¥1 ! ( ¥ - ¥ . ) sinned . = It E⇐tnx ) t ÷ f

÷ - 3¥.) cos na da

- I=÷a¥iinni- ÷sina.ae=n÷.

Ecco.n.it?-#.tiosn.a.

= I;÷ = kt ②n

3 it 3

*12 ( - 1)

htt

glass Z sinnx ⇒ floes = ⇐ knfj'

sin C nlt x )①

n = I

c) f est C' do - a par Dirichlet o - a CVS vers f .

On a meme CVN eh CVU.

f est L'

, on a CV C2

-

①

di Porsevae : I

' II ,= ÷ CE,

- ¥ . )'

ex

Ii ÷=I÷÷C¥ .. :# - I s = .IT ②

ffy.gl= ⇐ '

sin in 'T . ) -- Eo c- ' '

r

•c - 1)

P it 3 ②⇒ I - = -

P = o ( 2 p ti ) 3 32

Exercise 2 114mL

1) a ) On a I Icn (f) I < A do - c g Cx ) = I Cn Cf ) e

" n "CVN ( en particulier g

est

continue ) . Pan an calc al v u en Cours ( inter version I - S ) on a Cn (g) = Can ( f ) ,done f=g ds L !

②

b) si ( f ) suite de Cauchy dans ACT ), alon € Ice Cfn ) - Cee Cfm ) I I ,

i. e .

la suite ( de suites ! ) ( C" ) est de Cauchy dam e' ( IN ) .

Done C" e-?E. can e

'

Banach.

Soil f= En Cheikh, aeons f E ACT ) el Hf"

- f Ha = Kc Cf' ) - che , → O

. ②k

c ) f = Tp Cp Cf ) e' '

P "

, g = Eg Cats ) e' '

9 "

,done fog = En I Cp Cf ) Ca Cg) e

" "( mod uit de

ptg = n Cauchy )

Hfglla E E ¥.

.

Icp Htt Kaos ) I = ( E Kp(f) 1) ( I Kalos ) I ) = Hflla Hglla . ②

d) Hf Ha = loot f) I t

¥ ,ht, I Cn Cf 'll

⇐ KOCHI t €2.

Iz )"

( ¥ .

ten H 'll' )

""

②

⇐I Coffs I t C ( [ Tf ' call' doc ) "

parParse val .

e) Soil few = In caff ) e

' in "

.

C'

est un poly none Trigo eh Hfn - f HA =

, n

I cuff ) I T, O

.①

21 a ) co = de = Ep

an = ¥ So"

a - ex ) cos inside = II fo"

sin nxdx = [ cos me ] ! '=

n:# a - cos Ya)

Cn -- net C I - cos Yee ) ②

b) I - cosx E et I - cosa I 2 done

⇐ late IF + ¥6 .# +2k¥

. .

'T ) ②

Bone C- ACT )

a ⇐ set. -

- I -

①k⇐

.,

÷ = eeoc 's ) bone'

-