The Official Handy-Dandy Academy Math Cheat Sheet Page 3
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1
2
3
4Domains of Inverse Trig Functions
Function
Domain
Range
arcsin
[−1, 1]
[−π/2, π/2]
arccos
[−1, 1]
[0, π]
arctan
all real numbers
[−π/2, π/2]
arctan
all real numbers
[0, π]
arcsec
(−∞, −1] ∪ [1, ∞)
[0, π]
arccsc
(−∞, −1] ∪ [1, ∞)
[−π/2, π/2]
Odd and Even
Odd
Even
sin
cos
tan
sec
cot
csc
Formal Rules of Differentiation
Function
Derivative
f + g
f + g
cf
cf
f g
f g + f g
f
f g − f g
2
g
g
f ◦ g
f ◦ g · g
n
n−1
f
nf
f
Taylor Polynomial If f is a function, its nth degree Taylor polynomial centered at x = a is
n
(k)
f
(a)
k
p
(x) =
(x − a)
n
k!
k=0
Newton’s Law of Cooling The rate of cooling of a body is proportional to the difference between the
ambient temperature and the temperature of the body.
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