Calculus
posted by George on .
Consider the function f(x)=sin(1/x)
Find a sequence of xvalues that approach 0 such that
sin (1/x)=0
sin (1/x)=1
sin (1/x)=1
Is sin sin (1/x)=0 and sin (1/x)=1 does not exist.
What is sin (1/x)=1 then.

sin (1/x) = 0 if 1/x = pi, which means x = 1/pi
sin (1/x) = 1 if 1/x = pi/2, which means x = 2/pi
sin (1/x ) = 1 if 1/x = 3 pi/2, which means x = 2/(3 pi)
I don't understand why the x values should approach zero, or what the rules of the sequence are.