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2021-05-07
常用的等价无穷小
book
高等数学
#math
Headings
常用的等价无穷小
Tags
book
math
高等数学
book
math
高等数学
常用的等价无穷小
J.Gong
2021-05-07
0.31min
常用的等价无穷小
lim
x
→
0
sin
x
∼
x
lim
x
→
0
tan
x
∼
x
lim
x
→
0
arcsin
x
∼
x
lim
x
→
0
arctan
x
∼
x
lim
x
→
0
ln
(
1
+
x
)
∼
x
lim
x
→
0
(
e
x
−
1
)
∼
x
lim
x
→
0
(
a
x
−
1
)
∼
x
ln
a
lim
x
→
0
(
1
−
cos
x
)
∼
1
2
x
2
lim
x
→
0
[
(
1
+
x
)
a
−
1
]
∼
a
x
\lim_{x \to 0}\sin x \sim x \\ \lim_{x \to 0}\tan x \sim x \\ \lim_{x \to 0}\arcsin x \sim x \\ \lim_{x \to 0}\arctan x \sim x \\ \lim_{x \to 0}\ln(1+x) \sim x \\ \lim_{x \to 0}(e^x-1) \sim x \\ \lim_{x \to 0}(a^x-1) \sim x\ln a \\ \lim_{x \to 0}(1-\cos x) \sim \frac{1}{2} x^2 \\ \lim_{x \to 0}[(1+x)^a-1] \sim ax
x
→
0
lim
sin
x
∼
x
x
→
0
lim
tan
x
∼
x
x
→
0
lim
arcsin
x
∼
x
x
→
0
lim
arctan
x
∼
x
x
→
0
lim
ln
(
1
+
x
)
∼
x
x
→
0
lim
(
e
x
−
1
)
∼
x
x
→
0
lim
(
a
x
−
1
)
∼
x
ln
a
x
→
0
lim
(
1
−
cos
x
)
∼
2
1
x
2
x
→
0
lim
[(
1
+
x
)
a
−
1
]
∼
a
x
