Consider the function f(x) = sin(1/x).(a) Find a sequence of x-values that approach 0
Chapter 1, Problem 75(choose chapter or problem)
Consider the function f(x) = sin(1/x).(a) Find a sequence of x-values that approach 0 suchthat sin(1/x)=0.[Hint: Use the fact that sin() = sin(2) =sin(3) = ... = sin(n)=0.](b) Find a sequence of x-values that approach 0 suchthat sin(1/x)=1.[Hint: Use the fact that sin(n/2) = 1 if n =1, 5, 9,....](c) Find a sequence of x-values that approach 0 suchthat sin(1/x) = 1.(d) Explain why your answers to any two of parts (a)(c) show that limx0sin(1/x) does not exist.
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