Calculus
posted by George
Consider the function f(x)=sin(1/x)
Find a sequence of xvalues that approach 0 such that
(1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0}
(2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...}
(3) sin (1/x)=1
(4) Explain why your answers to any of parts(13) show that lim X>0 sin(1/x) does not exist.
Is sin sin (1/x)=0 and sin (1/x)=1 does not exist.
What is sin (1/x)=1 then.
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