λ x − ln x x 2. (Eexo146.tex) λx 2 + x 4 3. (Eequadiff14.tex)

FEUILLE DE CALCUL RAPIDE 7 janvier 2019

1.

(Eexo150.tex)

λ x − ^ln _x ^x 2.

(Eexo146.tex)

λx ² + x ⁴ 3.

(Eequadiff14.tex)

x → e ^x

2 (cos x − sin x) + λe ^x + µe ^2x , (λ, µ) ∈ R ²

4.

(Eexo151.tex)

λx + x sin x 5.

(Eexo155.tex)

λe ^2x + µe

^x2

6.

(Eexo154.tex)

λe ^−x + µe ^−3x 7.

(Eexo152.tex)

λe ^x + µe ^−2x 8.

(Eequadiff3.tex)

i − 1

2 e ^−t + λe ^it (λ ∈ C ) 9.

(Eequadiff13.tex)

x → − e ^x

2 (cos x + sin x) + λe ^x + µe ^2x , (λ, µ) ∈ R ²

10.

(Eequadiff6.tex)

(argsh(x) + λ)(x + p

x ² + 1) λ ∈ R 11.

(Eequadiff5.tex)

( t

2 + λ)e ^it + i

4 e ^−it λ ∈ C 12.

(Eexo156.tex)

e ^−x (λ cos 3x + µ sin 3x) 13.

(Eequadiff10.tex)

1

2 x ² + ln x − 2x 14.

(Eexo149.tex)

λ

x

15.

(Eequadiff4.tex)

2 ln(1 + x) + λ 1 + x λ ∈ R 16.

(Eequadiff7.tex)

− 1 3 e ^{3 cos x} 17.

(Eexo147.tex)

λ(2x + 1)

18.

(Eequadiff8.tex)

1 2 sin(x ² ) 19.

(Eequadiff17.tex)

t 7→ −(t ³ + 3t ² + 6t + 6)e ^−t 20.

(Eequadiff15.tex)

n x → p

1 + x ⁴ + λ(1 + x ⁴ )

¹⁴

, λ ∈ R o

21.

(Eexo157.tex)

λ cos 2x + µ sin 2x 22.

(Eequadiff11.tex)

1

3 + ln 3 e ^3x 3 ^x 23.

(Eequadiff2.tex)

1 + i

2 e ^t + λe ^it (λ ∈ C )

24.

(Eexo153.tex)

e ^2x (λ cos x + µ sin x) 25.

(Eexo158.tex)

λ cos ωx + µ sin ωx 26.

(Eexo148.tex)

λ cos x

27.

(Eequadiff1.tex)

1 2 + 1

10 cos(2t) + 1

5 sin(2t) + λe ^−t (λ ∈ R ) 28.

(Eequadiff16.tex)

t 7→ 1

2 (cos t + sin t)e ^t 29.

(Eequadiff12.tex)

1

2 arctan(x ² + 1) 30.

(Eequadiff9.tex)

1

2 x ² + 3x

¹³

+ 12 7 x

⁷⁶

1 ACEquadiff