CORRECTION DU CB N°7 i)

CORRECTION DU CB N°7

i) DL5

(

)

( )

ii) DL4

ln(1 ) ( )

x ch x

 + 

 

  = ^x−1₂^x2−1₆^x3+0.x4+o0

( )

iii) DL5 cos 1

x x

  

 

 

−

 

  = ¹⁻¹₂^{x2− −x3 35}₂₄^x4−11₆ ^x5+o0

( )

iv) DL5

2 ( 2)

4

1 x e^x x

 + − 

 

 

 

= ^{− −1}₂ ¹₆^x2−₂₄^{1 x4+o0}

( )

v) DL₃ sin x x

 

 

 

  = ¹⁻₁₂^{1 x2+0.x3+o0}

( )

CORRECTION DU CB N°7

i) DL5

(

)

( )

ii) DL4

ln(1 )

1 ( )

x sh x

 − 

 

 +  = ^{− +x 1}₂^x2−5₆^x3+3₄^x4+o0

( )

iii) DL5 sin 1

x x

  

 

  + 

  = ^{x− +x2 5}₆^x3−1₂^x4+₁₂₀^{1 x5+o0}

( )

iv) DL5 ²

(

)

4

ln 1

x x

x

 − + 

 

 

 

= ¹₂⁻¹₃^x2+1₄^x4+0.x5+o0

( )

v) DL₃ sh( )x x

 

 

 

  = ¹⁺₁₂^{1 x2+0.x3+o0}

( )