Hello Class, today we're going to be talking about limits. What are limits you ask?

The limit of f(x) is L as x approaches a. 



lim f(x) = L means that by taking a value of x very x->a close, but 

not equal, to a, the function value f(x) will be very close to L.  

Example:

From this graph we can see that as X comes in from the left side (positive infinity) it approaches 0. Likewise we also see that as X comes in from the right side (negtive infinity, it approaches 0). 

 

NOTE that you can also interpret this graph in different ways. Instead of x approaching infinity, maybe it approaches 0. How is the limit different then?

As x approaches 0 from the negative sector, we see that it approaches negative infinity but as x approaches 0 from the positive sector, it approaches positive infinity so in that circumstance THE LIMIT DOES NOT EXIST (https://www.youtube.com/watch?v=Lck5_YoxxGI) because they don't match. 

More examples:

What's the limit of F(x)= (x^2-9)/(x-3) as x approaches 3



Looking at the graph we see that as x approaches 3 it comes close to equaling 6