Definition of a limit

#incomplete

• add some graphical examples

The limit of a function is that function's value as it gets closer and closer to a specific x-point.

When working with function you have an independent and dependent variable. The limit is an approximation of what the dependent output will be given an independent input. For example what will be the output of when ?

As you can see finding the answer is problematic, so instead of jumping right to the variable in question () we instead we can inch closer and closer (we can find the output at , then , then , etc.), this action is called taking the limit. We do the from both the left and right side of the graph (start on the other size of : , , ), if both the numbers agree then we say that the limit exists (proving-limit-exists) if they are different numbers we say that the limit does not exist proving-limit-DNE.

• proving-limit-DNE
• proving-limit-exists