Analyse TD 2 - IMJ-PRG

2
1.ln(x+√1 + x2) + ln(√1 + x2−x) = 0
2. x√x= (√x)xR
1.tan(arcsin x) sin(arccos x) cos(arctan x)x
2. x
arctan x+ arctan 2x=π
4
arcsin 2x−arcsin x√3 = arcsin x
3.sin (π
8),tan ( π 12) cos (2π 5)
cos (−
4π
5) = cos ( 6π 5)
sh ch th
x∈R
sh x=ex−e−x
2,ch x=ex+e−x 2,th x=sh x ch x,
1.0
ch2−sh2= 1
2.argsh argch argth
1
3.ch(a+b)a b
sh(a+b)

1.
2.∗R+x > 1f(nx) 0 f
0
f
3. f R R x f(x) = 1 f(x) = 0 f
4.∗f:R→R1 0 1
q
p
qfQ
R−Q
5. f R0
∀x∈R, f(2x) = f(x).
f
x2+ 1
sin2x0
xE 1
x!0+
tan 3x
sin x0
th(arctan x) +∞
sin 1
x0+
xx0+
x+ 2
x2ln x0