Epsilon Delta Definition of the Limit
Move the epsilon slider to set a "target" for the values around the limit (which is 2 in this case). Try to find a value of delta so that, for any value of x in the interval around 1 (on the x-axis), the function value lies on the green line. Verify this by using the h slider.
The limit as x approaches c of a function f is equal to L if, for any interval around L determined by positive value epsilon, we are able to find an interval around c determined by positive value delta so that every value of x in the interval (except possibly at c itself) has a function value in the epsilon interval.