In Calculus, a limit is used to describe the value that a
function approaches as the input of that function approaches a
certain value. There are two ways to determine a Calculus limit:
a numerical approach or a graphical approach. In the graphical
approach, we analyze the graph of the function to determine the
points that each of the one-sided limits approach. I want to
talk about one sided limits, here's a function g of x equals and
it's piece y is defined x+8 for x less than -4 and x squared -1
for x greater than or equal to -4. Describe its behavior as x
approaches -4 well at -4 that's where the two pieces are kind of
joined together and so it may behave differently depending on
what side of -4 we're on. So let's try approaching -4 from the
left -5 is to the left of -4 on the number line so we're
starting from the left and moving to the right. Uh -5, -4.1,
-4.01 look what happens to the values we get 3, 3.9, 3.99 these
values are getting closer and closer to 4. When x is less than
-4 we're using this piec