Limits of Composite Functions - Part I

This video does not address what to do if the interior function is approaching a value horizontally, nor what to do if the interior function approaches two different values. The lesson linked below addresses both of those situations. If you feel this original lesson helped you out, go ahead and watch Part II.
• Limits of Composite Fu...

[@cholakol4284]

This has completely saved me from a lot of questions I had. What a life saver!

[@Cheezeraven]

Running through the Khan Academy course for Calculus right now and this was honestly a life saver -- Thanks

[@sankalps.9775]

yeah the khan academy video is not great at explaining it

[@yorickhunt570]

I don't know if I just missed it or my teacher didn't really explain the above + and below - thing that well. THANK YOU! (My tiny brain probably just didn't understand her)

[@chrisx2342]

Very clear, very helpful

[@JamesMcQuiston]

THANK YOU SO MUCH

[@armorman3005]

Very good explanation!

[@anony4717]

Thank you sir

[@yewande7464]

This was incredibly helpful thank you!!

[@AdityaSingh-zm1yd]

hey man what if there is a flat line ( for the function composed ), how would we decide from "above" or "below" then ?

[@MathLeagueofAmerica]

Whoops....I didn't see this comment until now. I actually just recently uploaded a Part 2 lesson for these limits. The link is in this video's description.

[@Xardas_]

The terminology of a limit coming from above or below is better explained in this video.

[@trm3177]

I'm an AP Calc teacher and I was wondering if you make your own resources? If you don't, where do you get the resources you used for this video.

[@MathLeagueofAmerica]

I somehow missed this comment. I generally make all my resources. For this video I used Desmos to generate the graphs and I just copied them onto the SMART notebook software. If you're looking for a great source of materials I strongly recommend you join the AP Calculus Teachers Facebook group. I've been teaching AP Calculus for 18 years but only recently found that group and I've probably learned more about teaching Calculus as well as getting some awesome materials in my time on that group as I did all the years prior.

[@georb3989]

very very great!

[@sentientmicrowave4831]

what if the limit doesn't approach from up or down, meaning y=a(a is constant)?

[@georb3989]

yeah i was wondering about this as well!

[@GrapJack]

I would think that means it's just a 2-sided limit. AKA, the same procedure as when it approaches from above on one side, and below from the other side.

[@frogmouth1416]

No actually in that case there is no limit, since it isn’t approaching anything. In that case you would just take f(that value) and not use a limit.

[@MathLeagueofAmerica]

I know my reply is WAY too late to be of any use to you, but in case other people see this comment and are wondering the same thing I finally got around to uploading a Part 2 to this lesson. Part 2 addresses this exact situation. In short, @frogmouth1416 is correct. If in the case of f[g(x)] the interior piece is not approaching from above or below you can find the final answer by simply doing f(whatever value g is approaching). For a more detailed explanation you can watch my Part 2 video, which I added to the description of this video.

[@junezhu5256]

Thank you for saving my ass