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2021-05-08
泰勒公式
book
高等数学
#math
Headings
泰勒公式
Tags
book
math
高等数学
book
math
高等数学
泰勒公式
J.Gong
2021-05-08
0.35min
泰勒公式
sin
x
=
x
−
x
3
3
!
+
o
(
x
3
)
\sin x = x - \frac{x^3}{3!} + o(x^3)
sin
x
=
x
−
3
!
x
3
+
o
(
x
3
)
cos
x
=
1
−
x
2
2
!
+
x
4
4
!
+
o
(
x
4
)
\cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} + o(x^4)
cos
x
=
1
−
2
!
x
2
+
4
!
x
4
+
o
(
x
4
)
arcsin
x
=
x
+
x
3
3
!
+
o
(
x
3
)
\arcsin x = x + \frac{x^3}{3!} + o(x^3)
arcsin
x
=
x
+
3
!
x
3
+
o
(
x
3
)
tan
x
=
x
+
x
3
3
+
o
(
x
3
)
\tan x = x + \frac{x^3}{3} + o(x^3)
tan
x
=
x
+
3
x
3
+
o
(
x
3
)
arctan
x
=
x
−
x
3
3
+
o
(
x
3
)
\arctan x = x - \frac{x^3}{3} + o(x^3)
arctan
x
=
x
−
3
x
3
+
o
(
x
3
)
ln
(
1
+
x
)
=
x
−
x
2
2
+
x
3
3
+
o
(
x
3
)
\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} + o(x^3)
ln
(
1
+
x
)
=
x
−
2
x
2
+
3
x
3
+
o
(
x
3
)
e
x
=
1
+
x
+
x
2
2
!
+
x
3
3
!
+
o
(
x
3
)
e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + o(x^3)
e
x
=
1
+
x
+
2
!
x
2
+
3
!
x
3
+
o
(
x
3
)
(
1
+
x
)
α
=
1
+
α
x
+
α
(
α
−
1
)
2
!
x
2
+
o
(
x
2
)
(1+x)^\alpha = 1 + \alpha x + \frac{\alpha(\alpha -1)}{2!}x^2 + o(x^2)
(
1
+
x
)
α
=
1
+
α
x
+
2
!
α
(
α
−
1
)
x
2
+
o
(
x
2
)
