test s2

2
f g h
•f(t) = 2 cos(2t)
•gt) = 1 + 2 sin(2t)
•h(t) = 2 cos(2t) + 2 sin(2t)
4
3
√x x1
3
x3
√−8 = −2
f x Rf(x) = 3
√2x2−x3
x7→ 3
√xR∗x7→ 1
3x2
3
f(x)>0⇔x62
(1 + u)1
31 + u
3+u2 9+u2ϵ(u)
f y =−x+2
3+∞

∀t∈R,cos(5t) = P(cos(t))
S= (cos(t) + jsin(t))5
cos(5t) = (S)
(a+b)5=a5+ 5a4b+ 12a3b2+ 12a2b3+ 5ab4+b5
(S) = cos5(t) + 10 cos3(t) sin2(t)−5 cos(t) sin4(t)
P(X) = 16X5−20X3+ 5X
2
I=∫1
0
x−xx
J=∫1
0
√1−x2x x = sin t
5
[0; +∞[
v(t) + τv(t)
t=E2v(0) = −E1
τ
t7→ E2
L[E2](p) = ∫+∞
0
E2
−pt t(p)>0L[E2](p) = E2
p
v(t) = −(E1+E2)
−t
τ+E2t∈[0; +∞[
v[0; +∞[
v[0; +∞[
t v(t) = E2
2
v
0v+∞

4
un=3n+ 1
4n+ 1
vn=3n
n!
+∞
∑
n=1
1
n(n+ 1)
+∞
∑
n=1
1
n(n+ 1) = 1
+∞
∑
n=1 (2
3)n
= 2
3
[0; +∞[
(E1)y′= 3y+ 6 y(0) = −1
(E2)x′′(t)+3x′(t)+2x(t) = t
1
10−3ln(1,1)