As a calculus teacher, I love creating my own calculus problems and this crazy limit problem is my creation today. I wanted to put this on my Calculus 1 quiz this week but I decided not to because it’s only week 3. So I am making a video on it! We have the limit of 1/(1-cos(ln(sin(tan^-1(e^(x^2)))))) as x goes to infinity. What’s the answer?
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You could get the sign just by looking at the outer cosine function. It has to be 1- because cosine can't be 1+ in the real world.
Beautifully explained Sir. plz make more of these simple questions that get people to understand concepts.
This video helped alot thanks!
Nice.
now prove it using M-N def.
limit does not exist as infinity is not a number
Pretty cool
Solve x^x=i
Calc 1 student here! I managed to follow along, but the whole 1+/1- thing is new to me. Maybe I missed it, but it feels like a useful detail to keep in mind if it comes up down the line. And now I know how to evaluate whether a limit goes to positive or negative infinity without using a blasted graph.
Kinda cool that I managed to keep up when I would have been deeply confused a month ago.
Wich religion you are from?
2:30 to 4:50 is useless here: cosine can't approach 1 from above anyway (especially, why do you even draw the trig circle here? what does it bring? from either side of pi/2 for sine or from either side of 0 for cosine, it's the same result)
A much cooler version is if the numerator is not 1, but e^(-4x^2). the answer is actually finite in that case !
As a student going to calculus, I’m scared
the answer is infinity
now multiply the denominator by x
I love these kinds of videos with a short fun problem, followed by an explanation!
This is really fun, the real thing about limits!
Any recommendations for learning calculus outside school?
I would prefer to change the order of the subtraction in the denominator, thus answer is negative infinity. Reason: If a student answers infinity, how do you know a sign analysis was made, not just doing a faulty solution? Giving the negative infinity answer shows the student did some reasoning to get the correct sign. OR WAS VERY LUCKY.
This one is deceptively easy, and you can also consider that cosine can only ever approach 1 from the left, because 1 is its maximum.
To solve this you have to know how those functions look. That's the real test here.
I’m a bit confused. Once you obtain 1/0, isn’t the limit determined to not exist?
why is it not 0 + ?
Does the limit exist? My guess is that it goes to positive infinity, and I guess it can’t go to negative infinity since the x^2 means the entire thing is always approaching from the same side
… the seven deadly sins on your shirt 🙂
Les't put 0 istead of the 1 on the top 😆
Hi Dr.!
This was nifty! You should definitely put it on your test at some point — math favors the bold.
i finally got a anser wright i just dindt know about the tan-1 thing but otherwise i would of gotten it without help
Plz do a M-N proof for the limit now .