Stage de pré-rentrée PCSI 2014 - 2015

f f(x) = 2
ex−1
f
g g(x) = ln 1−x
1 + x
g(x) = −1 [0,1[
f(x) = 3x+ 1
23
g(x) = 1
(3x2+ 1)7
h(x) = p2 + sin(x)
u(x) = v(5x−4) v
θ
k∈Zθ∈R
cos(θ) sin(θ)θ+π
θ+kπ k ∈Z
cos(θ) sin(θ)π
2+θ
π
2−θ
π
8
x∈[0,2π[ cos(x)−√3 sin(x) = 1
(un)n∈Nu0= 2 un+1 =1
2un+ 3
u1u2u3
(vn)n∈Nvn=un−6 (vn)
(vn) (un)
S(un)
n
X
i=1
i=n(n+ 1)
2
n
n
(3 + 2i)(1 −i)−(2 + i)2(1 + i)59−4i
2 + i
−2i1−i√3√3 + 3i1 + i√3
√3 + i
λ∈Rz= (λ+i)(λ+ 5 −i(λ−7))
n∈N(1 + i)n
C
2z2−5z+ 7 = 0 2iz −z+ 4 −i=z−i2z+ (3 + i)z= 4 −i