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Common Maclaurin series:
x2 x3
e =1+x+
+
+ ···
2
6
∞
X
xk
, for − ∞ < x < ∞
=
k!
x
k=0
x3 x5 x7
sin(x) = x −
+
−
+ ···
3!
5!
7!
∞
X
(−1)k x2k+1
=
, for − ∞ < x < ∞
(2k + 1)!
k=0
x2 x4 x6
+
−
+ ···
2!
4!
6!
∞
X
(−1)k x2k
=
, for − ∞ < x < ∞
(2k)!
cos(x) = 1 −
k=0
x2 x3 x4
ln(1 + x) = x −
+
−
+ ···
2
3
4
∞
X
(−1)k+1 xk
=
, for − 1 < x ≤ 1
k
k=1
x3 x5 x7
arctan(x) = x −
+
−
+ ···
3
5
7
∞
X
(−1)k x2k+1
=
, for − 1 ≤ x ≤ 1
2k + 1
k=0
Common trigonometric identities:
cos(x)2 + sin(x)2 = 1
sec(x)2 − tan(x)2 = 1
sin(2x) = 2 cos(x) sin(x)
cos(2x) = cos(x)2 − sin(x)2
cos(2x) = 2 cos(x)2 − 1
cos(2x) = 1 − 2 sin(x)2
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