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Limit viewed as a Microscope with Scratched lens

Limit as a microscope

In this geogebra file, we explore an analogy that views a limit as a microscope with a scratched lens. Our function serves as our specimen, and we can adjust where to focus the microscope by using "the dial" . In the dialog box, pick any function to examine and its graph will be shown in the bottom window. By clicking the "zoom" checkbox, you start looking in the microscope. Adjusting the c-slider changes where the "microscope" focuses. Remember however, that limits cannot see what happen at the input c, so in our analogy we must consider the lens of our microscope scratched. Clicking the "limit" checkbox puts the appropriate scratch over the lens. This is a nice way to get students to graphically visualize what a "limit" is doing.