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Epsilon-Delta Definition of a Limit - Case Study: f(x) = sin(1/x)

For the function f(x) = sin(1/x), consider lim_{x -> 0} sin(1/x)$. Try the demo below to see that if ε is less than 1, we cannot find a corresponding δ such that if |x - 0| < δ, then |f(x) - 0| < ε. Hence the limit does not exist.
Use the sliders to change the values of δ and ε.