How to find horizontal asymptote, vertical asymptote, & removable discontinuity (calc 1 tutorial)

This calculus tutorial helps you to learn how to find the horizontal asymptote, vertical asymptote, & removable discontinuity. For H.A., we take the limit as x goes to infinity. For V.A. we pay attention to nonzero/0. For R.D. we pay attention to 0/0.

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#blackpenredpen #math #calculus #apcalculus

Horizontal Asymptote, 0:10
Vertical Asymptote 4:16
Removable Discontinuity 6:47
The graph 10:03

[arequina]

It's been over 25 years since I've done calculus. However, every time I watch this show, I am always amazed at it's power. Even more amazed at the simplicity of how it is taught by this professor. I truly love your show.

[MrFedX]

Great video! I often feel that there’s a disconnect between teaching the theory of limits and actually calculating limits. In this video you made a really good job combining the two. Made me go ”ahaaa!” a few times. :)

[leronm]

This video was a great help! I couldn’t figure out what the difference between a vertical asymptote and a removable discontinuity for the life of me!

[farespasuni]

I just love physics more and more when i see your videos

[Chiinox]

What about oblique (diagonal) asymptotes of a function? Just curious, thanks for any responses :)

[willful]

thanks for the refresher, i'm starting uni next monday!

[ThePowerfulOne]

I remember learning about HA and VA in pre-calculus in college. Fun times!!!

[nuji]

Nice Video! Just in time for final exam period for many students taking summer term!

[snejpu]

How about the third kind of asymptotę: y=ax+b?

[joso]

Hey man great video, could you make one proving that π is irrational?

[JefiKnight]

That blows my mind that (3x-6)/(x²+x-6) and 3/(x+3) have different values at x=2. The are equivalent formulas because you multiply the top and bottom by the same thing. But not really?

[johnadrias]

Thankyou now i ferfect the quiz because of your video

[si]

can u do a video on finding asymptotes in case of polar coordinate system?

[matthewstevens]

Could you do a video on sketching rational function?

[JeffreyLByrd]

I’m a little perplexed as to why you didn’t just factor the top and bottom and cancel the (x-2) in the first place. To me it makes the whole problem easier.

[calyodelphi]

So, here's a fun (and probably difficult) set of questions: It's known that hyperbolic functions have sloped asymptotes. But is it possible for a function to have a non-linear asymptote? If yes, can you cite and demonstrate an example? If no, is there a proof that you can cite and demonstrate for it? :)

[Sainep]

عفوا ..هل تستطيع اعطاء دروس جامعية ام لا ؟

[herowise]

Can u find the asymptotes that limits us to approach each other? yes its the internet

[ligleaper]

That last part I did LH quickly in my head to find 3/5 lol

[charlottedarroch]

The function f(x) = (3x-6)/(x^2+x-6) doesn't have a removable discontinuity at x = 2. It is defined there and it is continuous there. As you demonstrated in the video, f(x) = (3x-6)/(x^2+x-6) = 3(x-2)/((x+3)(x-2)) = 3/(x+3), so f(2) = 3/5. It would be a removable discontinuity if f(x) were defined in a piecewise way such that f(x) = (3x-6)/(x^2+x-6) for x =/= 2 and f(2) was equal to something other than 3/5.