Visualizing Limits Graphically

Notes:

(1) The x limit point can be adjusted using the orange "a" slider.
(2) Initial values for "x" to the left and right of "a" can also be set using sliders.
(3) Point "F" representing f(a) can be moved by dragging the point vertically.
(4) The initial presentation of the function is as 2 pieces with a jump separation at "a". This allows for the presentation of differing left and right limits. Text popups appear as the "x" reaches it's limit at "a" from either the left or the right. If both left and right limits have been reached a third popup shows indicating the status of the general limit.
(5) To have the left and right limits equal each other, set the Jump Height slider to zero.

Fred Mueller, Created with GeoGebra