1，
x
∼
tan
x
∼
sin
x
∼
arcsin
x
∼
(
e
x
−
1
)
∼
arctan
x
∼
l
n
(
1
+
x
)
∼
l
n
(
x
+
1
+
x
2
)
x\sim \tan x\sim \sin x\sim \arcsin x\sim (e^x-1)\sim\arctan x\sim ln(1+x)\sim ln(x+\sqrt{1+x^2})
x∼tanx∼sinx∼arcsinx∼(ex−1)∼arctanx∼ln(1+x)∼ln(x+1+x2) 2，
(
1
−
cos
x
)
∼
1
2
x
2
(1-\cos x)\sim\frac{1}{2}x^2
(1−cosx)∼21x2 3，
l
o
g
a
(
1
+
x
)
∼
x
l
n
a
log_a(1+x)\sim\frac{x}{lna}
loga(1+x)∼lnax 4，
(
x
−
sin
x
)
∼
1
6
x
3
∼
(
arcsin
x
−
x
)
(x - \sin x)\sim\frac{1}{6}x^3\sim(\arcsin x-x)
(x−sinx)∼61x3∼(arcsinx−x) 5，
(
tan
x
−
x
)
∼
1
3
x
3
∼
(
x
−
arctan
x
)
(\tan x -x)\sim\frac{1}{3}x^3\sim(x-\arctan x)
(tanx−x)∼31x3∼(x−arctanx) 6，
(
1
+
b
x
)
a
−
1
∼
a
b
x
(1+bx)^a-1\sim abx
(1+bx)a−1∼abx 7，
(
tan
x
−
sin
x
)
∼
1
2
x
3
(\tan x-\sin x)\sim \frac{1}{2}x^3
(tanx−sinx)∼21x3 8，
a
x
−
1
∼
x
l
n
a
a^x-1\sim xlna
ax−1∼xlna 9，
(
1
+
x
n
−
1
)
∼
x
n
(\sqrt[n]{1+x}-1)\sim \frac{x}{n}
(n1+x−1)∼nx
