Asked by Emily
f(x)=cos(1/x)
Find a sequence for x-values that approach 0 such that cos(1/x)=0.
Find a sequence for x-values that approach 0 such that cos(1/x)=0.
Answers
Answered by
Steve
cos u = 0 when u = an odd multiple of π/2.
So, we want 1/x = kπ/2 for odd k
x = 2/kπ
x = 2/3π 2/5π 2/7π ...
the sequence approaches 0, and cos(1/x) = 0 for each x.
So, we want 1/x = kπ/2 for odd k
x = 2/kπ
x = 2/3π 2/5π 2/7π ...
the sequence approaches 0, and cos(1/x) = 0 for each x.
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