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5
1999 Calculus #5: Continuous Fraction
1999 Calculus #5: Continuous Fraction
Source:
June 21, 2012
calculus
quadratics
algebra
quadratic formula
Problem Statement
Let
f
(
x
)
=
x
+
1
2
x
+
1
2
x
+
1
2
x
+
⋯
f(x)=x+\cfrac{1}{2x+\cfrac{1}{2x+\cfrac{1}{2x+\cdots}}}
f
(
x
)
=
x
+
2
x
+
2
x
+
2
x
+
⋯
1
1
1
. Find
f
(
99
)
f
′
(
99
)
f(99)f^\prime (99)
f
(
99
)
f
′
(
99
)
.
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