Problem:
The number of x-intercepts on the graph of y=sin(1/x) in the interval (0.0001,0.001) is closest to
Answer Choices:
A. 2900
B. 3000
C. 3100
D. 3200
E. 3300
Solution:
The intercepts occur where sin(1/x)=0, that is, where x=1/(kπ) and k is a nonzero integer. Solving
0.0001<kπ1<0.001
yields
π1000<k<π10,000
Thus the number of x intercepts in (0.0001,0.001) is
⌊π10,000⌋−⌊π1000⌋=3183−318=2865
which is closest to 2900.
The problems on this page are the property of the MAA's American Mathematics Competitions