In many cases, the limit as x approaches c and the actual value of f(c) are the same. For example, the limit as x approaches 5 for f(x) = x²is 25, and the same as f(5) = 25. You can verify the limit is 25 by constructing a table, where you cansee the limit approaching 25.

In some cases, the actual value of f(x) is different from it limit. For example, for the piecemeal function defined as f(x) = x² for x3 andf(x) =-2 for x = 3, the limit as x approaches 3 is 9, but the actual value of f(3) = -2 by the definition.

In another example, the limit does not appear to exist, but it does:

f(x) = (x-2)/((x² - 4) <-- from a table, or graph, we can see the limit as x approaches 2 is 1/4, but the value of f(2) is undefined.

Find an example where the limit as x approaches some specific number, c, is the same as f(c). Be sure to state both the limit and the f(c). Then find an example where the limit and the f(c) are different. Again, state the limit and the f(c). Lastly, in your own words, show how you would explain to someone the concept of limits, and how it relates tof(c) .