Epsilon-Delta Definition of a Limit - Case Study: f(x) = sin(x) / x
For the function f(x) = sin(x)/x, we saw before that it looked like the limit of f(x) at 0 was 1. Try the demo below to see that no matter what ε is, we can always find a corresponding δ such that if |x - 0| < δ, then |f(x) - 1| < ε.
Use the sliders to change the values of δ and ε.
It should be clear from the picture that we can always choose a δ that works for this function at 0, even though f(0) = sin(0) / 0 is not defined. We say that the limit of f(x) as x approaches 0 is 0. We will prove this later in the course.