Difference between revisions of "1999 AHSME Problems/Problem 18"
(New page: == Problem == How many zeros does <math>f(x) = \cos(\log x)</math> have on the interval <math>0 < x < 1</math>? <math> \mathrm{(A) \ } 0 \qquad \mathrm{(B) \ } 1 \qquad \mathrm{(C) \ } 2 ...) |
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== See also == | == See also == | ||
{{AHSME box|year=1999|num-b=17|num-a=19}} | {{AHSME box|year=1999|num-b=17|num-a=19}} | ||
+ | {{MAA Notice}} |
Revision as of 14:35, 5 July 2013
Problem
How many zeros does have on the interval
?
Solution
For we have
, and the logarithm is a strictly increasing function on this interval.
is zero for all
of the form
, where
. There are
such
in
.
Here's the graph of the function on :
As we go closer to , the function will more and more wildly oscilate between
and
. This is how it looks like at
.
And one more zoom, at .
See also
1999 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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