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Basic Limit Ideas

Check out this geogebra applet to check your basic understanding of a limit.

Recognizing the Limit

This applet helps show where the limits of basic functions are. With basic functions you can usually just plug in the value of the x you are evaluating to find the limit, but what if your function is a little more complicated?

Consider the case where f(x) = ((x2) -2)/x-3

Looking at this we see that an asymptote exists at x=3. If we were to hand plot all the points of this function on a graph, there wouldn’t be a point at x=3. However, a limit is where a function intends to reach, so despite the fact that f(x) is undefined at x=3, there is still a limit.

Try f(x) = ((x2) -2)/x-3 in the geogebra applet to see what the limit is.

Long before Calculus had been invented, Archimedes used the idea of limits to find the area of a circle.
Who knew limits could be so helpful?
Check out this Geogebra Applet demonstrating what Archimedes was probably thinking.

Finding the Approaching Area