Proof of Limits of Functions
Instructions
Use this dynamic GeoGebra file to explore the definition of a functional limit. You can change the given information on the left. Note that the definition requires you specify: f(x), c, and L. Use the sketch to understand the meaning of the formal definition of functional limit, including what an " challenge" signifies, and what a sufficient " response" means.
Reflection Questions
Drag the sliders of and , graphically which area shows the definition "If for all , there exists a s.t. if 0<|x-c|<, then |f(x)-L|<"? Observe and try to conclude how would value changes corresponding to different values. You may also try some other functions other than the given one.