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4
2004 Calculus #4
2004 Calculus #4
Source:
November 29, 2011
calculus
trigonometry
algebra
polynomial
induction
Problem Statement
Let
f
(
x
)
=
cos
(
cos
(
cos
(
cos
(
cos
(
cos
(
cos
(
cos
(
x
)
)
)
)
)
)
)
)
f(x)=\cos(\cos(\cos(\cos(\cos(\cos(\cos(\cos(x))))))))
f
(
x
)
=
cos
(
cos
(
cos
(
cos
(
cos
(
cos
(
cos
(
cos
(
x
))))))))
, and suppose that the number
a
a
a
satisfies the equation
a
=
cos
a
a=\cos a
a
=
cos
a
. Express
f
′
(
a
)
f'(a)
f
′
(
a
)
as a polynomial in
a
a
a
.
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