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4
f:R→R
07→ 0
x7→ x3/2sin µ1
x¶.
5 0
f:R→R
x7→ Arctan(x).
4
f:R→R
x7→ x5+ 2.
5 0
g:R→R
x7→ Arctan(Arcsin(x)).
4
x y n
un=³1 + x
n+y n2´n.
6 0
g: [−1,1] →R
x7→ Arcsin(ex−1−x).
4
x y n
un=³1 + x
n+y n2´n2
.
6 0
g: [−1,1] →R
x7→ eArctan(x2).

4
f:R→R
x7→ e−(x−3)2.
½u0= 1
un+1 = Arctan(un),∀n∈N.
4
C2
4 0
g:R→R
x7→ Arctan(x) + Argsh(x).
4
5 0
g:R→R
x7→ sin(x) + Arcsin(x) + Arcsin(sin(x)).
4
lim
x→0
tan(x) + sin(x)
Arctan(x) + Arcsin(x),
lim
x→0
ex−e
log(1 + x).
f:R→R
x7→ xex+ Arctan(x)

4
g:R→R
x7→ ex−e−x.
3
0
f:R→R
x7→ Arcsin(x).
4
f:R→R
07→ 0
x7→ x5/2sin(1/x)x6= 0.
◦2
0f
◦f0
g:R→R
x7→ Arcsin(sin(x)).
4
[0,1]
1
4,1 2,3 4
lim
x→0
sin(x) + Arcsin(x)
tan(x) + Arctan(x),
lim
x→1log(x)e
1
(x−1)2,
lim
x→+∞
Arcsin(sin(1/x))
Arctan(tan(1/x)).
4
Arctan
lim
x→0
sin(x)
x+ tan(x),
lim
x→1
√x+ 1 −√2x
sin(πx),
lim
x→+∞
e1/x −e−1/x
e1/x2−e−1/x2.

4
lim
x→0
sin(x)
x2
lim
x→π
4
sin(x)−√2/2
cos(x)−√2/2.
fR→R
limx→+∞f(x) = 2 limx→−∞ f(x)=0
R
4
f:R→R
x7→ x5+ 1.
g:R→R
x7→ Arccos(cos(x)).
4
lim
x→π
4
tan(x)−1
xπ
4
,
lim
x→+∞³px3+ 1 −x√x´.
f:R→R
x7→ x3x < 0,
x7→ sin(x)x∈[0,π
2[,
x7→ log µ2ex
π¶x > π 2.
4
•Arctan(x) + Arctan( 1
x)x < 0
•E[|cos(x)|]E[a]
a
g:R→R
x7→ Arctan µlog(x2+ 1)
2 + cos2(x)¶.

4
[0,1]
R1
3
2
3
u0= 2
un+1 =une−un,∀n∈N.
4
f:R∗→R
x7→ x2sin 1
x5.
f: ]0,+∞[→R
x7→ Arctan(x).
g: ]0,+∞[→R
x7→ Arctan µ1
x¶.
4
lim
x→+∞
x3e−x/2,
lim
x→+∞
xlog µ1 + 1
x¶.
g
g:R→R
x7→ x4+x+ 1,
10−2
4
f g R→R
x∈R|f(x)|=|g(x)|
f g
h:R→R
07→ 0
x7→ x2sin µ1
x¶x6= 0.