I hope I get an A on my Calculus Exam!

Limits describe a function, f(x), and how it behaves, as x approaches a designated value, a. 

Graphically, a Limit can also describe what y value corresponds with x, as it approaches the value a. They can be written in the form:

Like the limit as x approaches 2, of f(x)= x:

Average rate of change is just the change in the function, or y, over the change in x!

Instantaneous rate of change is just the limit of average rate of change, as the change in x approaches 0!

The Instantaneous rate of change gives us the slope of the tangent line at that point!

These limits only happen, if the function comes to a real point on the graph, or the same value. In other words...

Continuity is awesome!

What if the function wasn't continuous, or had gaps in it's domain?

Woah! I see the jump, in jump discontinuity!

It never ends!!!

Weeee!

AAAAA!!!

What the...

I can determine if parts of these functions are continuous, if I only focus on the left or right!

Now I can evaluate limits i wouldn't have been able to before!

If the limit, when evaluated from both sides, equals the same value (in this case 0), then the function is continuous!!

Now I have reviewed how to evaluate limits, but how will I solve them for a value??

I want to help you, Sparky! I'll remind you of how to solve for limits!

Thanks, Bea! 

Let's solve for limits and review the different rules we have.

Solving for limits can be done graphically, algebraically, by substitution, and through L'Hopital's Rule.

For example:

If Sparky and I ran for a teddy at the same time following the pattern of a function, the moment we both reach the teddy is the limit.

If I am running towards the teddy and Sparky isn't, then the limit doesn't exist!