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How to Compute Limits

The symbol x in

limx→c f(x)

is an example of a "dummy variable." The value of the limit does not depend on x at all. However, it does depend on c. If we replace c by a variable u, we obtain a new function

L(u) = limx→u f(x).

A limit

limx→c f(x)

is usually computed as follows.

Step 1

Let x be infinitely close but not equal to c, and simplify f(x).

Step 2

Compute the standard part st(f(x)).

CONCLUSION If the limit lim f(x) exists, it must equal st(f(x)).
Home Continuous Functions Limits How to Compute Limits

Last Update: 2006-11-05