Your Teacher Is WRONG About This Limit⚠️

Hey, Number Ninjas! In this video, we'll uncover some misunderstandings around limits such as the limit of sin(1/x). Properties of the math function such as it oscillating, or simply the fact that we can't plug in 0 for x due to dividing by zero aren't conclusive enough to determine whether the limit exists. Teachers and students alike can sometimes trip on these important details about solving limits and by the end of this video, my goal is to help you understand the real reason the limit doesn't exist.

I do cover one case in the video about another domain-restricted function that I use to illustrate that simply lacking continuity at a point doesn't imply there's no limit for that point. Here's the video that further dives into that other example I used and it's again another video where I uncover some misunderstandings about whether x^2 / x is the same as x. Be sure to check it out for more useful details!

Here's yet another video of a common misunderstanding about using L'Hopital's rule that you'll want to definitely if you've ever used L'Hopital's rule to solve this famous squeeze limit problem:

Hope you enjoy this video! Be sure to like the video if it was useful to you and subscribe for more helpful tips on your next exam! Also, if you have any feedback for me, leave a comment below as it would help me better help you all out!

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📚Helpful stuff and my favorite MUST haves I used in my college courses ⬇️
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This graphing calculator is a beast and never failed me in college:

I loved THIS ruler in college, for engineering classes:

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[NumberNinjaDave]

In case of any confusion, I use the graph of sin x in this video, not sin(1/x), since it’s easier than the original problem. I recommend it as a strategy, especially if you don’t have a calculator!

I do cover one case in the video about another domain-restricted function that I use to illustrate that simply lacking continuity at a point doesn't imply there's no limit for that point. Here's the video that further dives into that other example I used and it's again another video where I uncover some misunderstandings about whether x^2 / x is the same as x. Be sure to check it out for more useful details!

Here's yet another video of a common misunderstanding about using L'Hopital's rule that you'll want to definitely if you've ever used L'Hopital's rule to solve this famous squeeze limit problem:

Hope you enjoy this video! Be sure to like the video if it was useful to you and subscribe for more helpful tips on your next exam! Also, if you have any feedback for me, leave a comment below as it would help me better help you all out!

Also, sorry about the random line on the screen after about the 5 minute mark

[kingbeauregard]

Because I love pain, I would try to epsilon-delta this thing and discover I cannot find a way to do it. The oscillations as x approaches 0 are so fast - and importantly, the range of the function remains -1 to 1 - it's impossible for epsilon to approach 0 as delta approaches 0 (at the value x = 0).

[kingforgotten]

Sin(x) does not equal 1 at 3pi/2 it is equal to -1.

[henryginn]

Doesn't this limit very clearly not exist? It's oscillating like crazy around 0? What would teachers be getting wrong about this?

[DirectedArt]

What i would do is to make a variable change θ=1/x, x->0 => θ->∞ so we have the limit when θ->∞ of sinθ. Now we do know that -1≤sinθ≤1 so we take the limit in all 3 parts of the inequality, and the limit of -1 and 1 is -1 and 1, respectively so the limit oscilates between -1 and 1 so the limit diverges

[ezraoctopus]

Can't you just say that as x goes to 0, the argument goes to infinity or negative infinity, and since sin oscilates as it approaches infinity and negative infinity, the limit doesn't exist?

[NumberNinjaDave]

Starting next week, Saturday video uploads will go back to 6AM MST instead of 6PM since it looks like you guys prefer that! Keep crushing it, ninjas!

[danieleforcella]

This limit is like asking "which came first: the chicken or the egg".

[archangecamilien]

Don't quite remember what teachers used to say, lol, for that one, but looking at it right now, I'm guessing it should be undefined...I mean...

[Bob-xmv]

Why do you work it out with 2pi n and not pi n, as sin (pi) is also zero?