Question

xplain how examining limits along different paths may show that a limit does not exist. Can we use this type of analysis to show that a limit does exist?

Answer 1

Examining limits along different paths can show that a limit does not exist if the limit approaches different values along different paths. However, it can also be used to show that a limit does exist if the limit approaches the same value along all paths.

Step-by-step explanation:

When examining limits along different paths, we can determine if a limit does not exist. If the limit approaches different values along different paths, then the limit does not exist. For example, if we have a function where the limit approaches 1 as x approaches 0 from the left, but approaches 2 as x approaches 0 from the right, then the limit does not exist. This type of analysis can be used to show that a limit does exist if the limit approaches the same value along all paths.