# Interactive video lesson plan for: Limits of composite functions - How to find them?

#### Activity overview:

► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course

In this video we’re talking about how to find the limit of composite functions.

0:33 // Two different ways to write a composite
1:01 // Two ways to find the limit of a composite: algebraically and graphically
1:28 // How to find the limit of a composite algebraically
4:10 // How to find the limit of a composite when you have the graphs
6:52 // Composites can be given as one function or as two functions (together vs. separately). How to split a composite function apart? How to create a composite function from two functions?
9:33 // Limit laws still apply when you’re finding the limit of a composite function
11:46 // An example with a rational function
15:46 // What to do when the limit doesn’t exist (DNE). What do you do when the one-sided limits are different? What if the inner function of the composite doesn’t have a general limit?
19:22 // What do do when the outer function of the composite doesn’t have a general limit?
20:44 // What to do when the graph doesn’t have a general limit, or the one-sided limits are different?

Remember that composite functions are “functions of functions”, which means that we have one function plugged into another function. As an example, sin(x^2) is a composite function because we’ve plugged the function x^2 into the function sin(x). Think of any function that as an “outer part” and an “inner part” as composite functions.

The most important thing to know about evaluating limits of composite functions is that we can do so algebraically or graphically. Basically that means we can do math to figure out the limit, or we can look at the graphs of the two functions (if we have them) and figure it out that way. In this video we’ll look at examples of both so that you know how to find the limit using math, and also how to find the limit just by looking at the graphs.

In either case, whether you’re looking at the limit algebraically or graphically, you’ll be finding the limit of the inside function, and then evaluating the outside function at the resulting value. So if you’re taking the limit as x goes to 0 of the composite f(g(x)), that means you’ll be finding the limit as x goes to 0 of g(x), and then taking whatever real-number result you got and plugging that number into f(x). Whatever you get will be the answer to the problem.

Music by Joakim Karud: http://soundcloud.com/joakimkarud

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

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