1-B One-Sided Limits
Instructions
Use the input boxes to enter formulas for the left (red) and right (blue) pieces of a piecewise defined function. (You can use the same function formula in both input boxes to get a "normal" graph.)
- Use the input box for c to change the point where you will investigate the limits.
- Use the input box for x to set a starting point for your investigation.
- Use the x \to c button to have x move closer to c.
- Use the Trace On / Off buttons to leave a trace of the function values on the y-axis to observe whether they approach a particular value. Use Clear Trace to remove all trace points.
- When the function values get "close enough" to the limit value, the one-sided limit notation will be displayed on the bottom-left of the screen.
1-B The Limit Concept (One-Sided Limits)
Informally, means that the function values f(x) get progressively closer to L the closer we let x get to c. In practice, we are typically concerned with determining whether a limit exists, and estimating its value, if it does exist. We do this by letting x approach c either from the left () or from the right () and observing the corresponding function values f(x). If the one-sided limits exist and are equal to the same number L, then the two-sided limit also exists and is equal to L.